[{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07330"}],"scopus_import":"1","citation":{"ama":"Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>","ieee":"J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023.","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics (2023).","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics.","mla":"Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>.","apa":"Chen, J., Kaloshin, V., &#38; Zhang, H. K. (2023). Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>","chicago":"Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>."},"publication_status":"epub_ahead","doi":"10.1007/s00220-023-04837-z","date_published":"2023-09-29T00:00:00Z","oa_version":"Preprint","oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"status":"public","ec_funded":1,"month":"09","year":"2023","date_updated":"2023-12-13T13:02:44Z","arxiv":1,"abstract":[{"lang":"eng","text":"In the paper, we establish Squash Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute the Lyapunov exponents along the maximal period two orbit, as well as the value of the Peierls’ Barrier function from the maximal marked length spectrum associated to the rotation number 2n/4n+1."}],"_id":"14427","article_processing_charge":"No","article_type":"original","external_id":{"isi":["001073177200001"],"arxiv":["1902.07330"]},"quality_controlled":"1","date_created":"2023-10-15T22:01:11Z","publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"department":[{"_id":"VaKa"}],"type":"journal_article","title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"29","acknowledgement":"VK acknowledges a partial support by the NSF grant DMS-1402164 and ERC Grant #885707. Discussions with Martin Leguil and Jacopo De Simoi were very useful. JC visited the University of Maryland and thanks for the hospitality. Also, JC was partially supported by the National Key Research and Development Program of China (No.2022YFA1005802), the NSFC Grant 12001392 and NSF of Jiangsu BK20200850. H.-K. Zhang is partially supported by the National Science Foundation (DMS-2220211), as well as Simons Foundation Collaboration Grants for Mathematicians (706383).","project":[{"grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"author":[{"first_name":"Jianyu","last_name":"Chen","full_name":"Chen, Jianyu"},{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"full_name":"Zhang, Hong Kun","first_name":"Hong Kun","last_name":"Zhang"}],"isi":1},{"page":"829-901","date_created":"2023-04-30T22:01:05Z","publication":"Inventiones Mathematicae","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"VaKa"}],"article_type":"original","article_processing_charge":"No","external_id":{"arxiv":["1905.00890"],"isi":["000978887600001"]},"volume":233,"quality_controlled":"1","acknowledgement":"J.D.S. and M.L. have been partially supported by the NSERC Discovery grant, reference number 502617-2017. M.L. was also supported by the ERC project 692925 NUHGD of Sylvain Crovisier, by the ANR AAPG 2021 PRC CoSyDy: Conformally symplectic dynamics, beyond symplectic dynamics (ANR-CE40-0014), and by the ANR JCJC PADAWAN: Parabolic dynamics, bifurcations and wandering domains (ANR-21-CE40-0012). V.K. acknowledges partial support of the NSF grant DMS-1402164 and ERC Grant # 885707.","day":"01","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"isi":1,"author":[{"full_name":"De Simoi, Jacopo","first_name":"Jacopo","last_name":"De Simoi"},{"last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim"},{"first_name":"Martin","last_name":"Leguil","full_name":"Leguil, Martin"}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","publication_status":"published","doi":"10.1007/s00222-023-01191-8","oa_version":"Preprint","date_published":"2023-08-01T00:00:00Z","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1905.00890","open_access":"1"}],"citation":{"short":"J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023) 829–901.","ama":"De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. <i>Inventiones Mathematicae</i>. 2023;233:829-901. doi:<a href=\"https://doi.org/10.1007/s00222-023-01191-8\">10.1007/s00222-023-01191-8</a>","ieee":"J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination of analytic chaotic billiards with axial symmetries,” <i>Inventiones Mathematicae</i>, vol. 233. Springer Nature, pp. 829–901, 2023.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones Mathematicae</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00222-023-01191-8\">https://doi.org/10.1007/s00222-023-01191-8</a>.","apa":"De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2023). Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-023-01191-8\">https://doi.org/10.1007/s00222-023-01191-8</a>","mla":"De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones Mathematicae</i>, vol. 233, Springer Nature, 2023, pp. 829–901, doi:<a href=\"https://doi.org/10.1007/s00222-023-01191-8\">10.1007/s00222-023-01191-8</a>.","ista":"De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 233, 829–901."},"intvolume":"       233","date_updated":"2023-10-04T11:25:37Z","arxiv":1,"abstract":[{"text":"We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.","lang":"eng"}],"year":"2023","_id":"12877","status":"public","oa":1,"publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"month":"08","ec_funded":1},{"_id":"12145","date_updated":"2023-08-04T08:59:14Z","abstract":[{"text":"In the class of strictly convex smooth boundaries each of which has no strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugate near their respective boundaries, and C∞-conjugate, near the boundary and away from a line passing through the center of the underlying ellipse. We also prove that, if the billiard maps corresponding to two ellipses are topologically conjugate, then the two ellipses are similar.","lang":"eng"}],"arxiv":1,"issue":"6","year":"2022","month":"10","ec_funded":1,"status":"public","publication_identifier":{"eissn":["1468-4845"],"issn":["1560-3547"]},"oa":1,"oa_version":"Preprint","date_published":"2022-10-03T00:00:00Z","publication_status":"published","doi":"10.1134/S1560354722050021","intvolume":"        27","citation":{"chicago":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1134/S1560354722050021\">https://doi.org/10.1134/S1560354722050021</a>.","ista":"Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537.","apa":"Koudjinan, E., &#38; Kaloshin, V. (2022). On some invariants of Birkhoff billiards under conjugacy. <i>Regular and Chaotic Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/S1560354722050021\">https://doi.org/10.1134/S1560354722050021</a>","mla":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:<a href=\"https://doi.org/10.1134/S1560354722050021\">10.1134/S1560354722050021</a>.","ama":"Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy. <i>Regular and Chaotic Dynamics</i>. 2022;27(6):525-537. doi:<a href=\"https://doi.org/10.1134/S1560354722050021\">10.1134/S1560354722050021</a>","ieee":"E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under conjugacy,” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6. Springer Nature, pp. 525–537, 2022.","short":"E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.14640","open_access":"1"}],"scopus_import":"1","project":[{"call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707"}],"isi":1,"author":[{"full_name":"Koudjinan, Edmond","first_name":"Edmond","orcid":"0000-0003-2640-4049","last_name":"Koudjinan","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E"},{"last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim","full_name":"Kaloshin, Vadim"}],"acknowledgement":"We are grateful to the anonymous referees for their careful reading and valuable remarks and\r\ncomments which helped to improve the paper significantly. We gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885707).","day":"03","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"On some invariants of Birkhoff billiards under conjugacy","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"VaKa"}],"page":"525-537","date_created":"2023-01-12T12:06:49Z","publication":"Regular and Chaotic Dynamics","external_id":{"isi":["000865267300002"],"arxiv":["2105.14640"]},"keyword":["Mechanical Engineering","Applied Mathematics","Mathematical Physics","Modeling and Simulation","Statistical and Nonlinear Physics","Mathematics (miscellaneous)"],"volume":27,"quality_controlled":"1","related_material":{"link":[{"url":"https://doi.org/10.1134/s1560354722060107","relation":"erratum"}]},"article_processing_charge":"No","article_type":"original"},{"citation":{"ieee":"V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles.” 2021.","ama":"Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles. 2021.","short":"V. Kaloshin, E. Koudjinan, (2021).","chicago":"Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles,” 2021.","apa":"Kaloshin, V., &#38; Koudjinan, E. (2021). Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles.","ista":"Kaloshin V, Koudjinan E. 2021. Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles.","mla":"Kaloshin, Vadim, and Edmond Koudjinan. <i>Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles</i>. 2021."},"ddc":["500"],"article_processing_charge":"No","file_date_updated":"2021-05-30T13:57:37Z","date_published":"2021-01-01T00:00:00Z","department":[{"_id":"VaKa"}],"language":[{"iso":"eng"}],"oa_version":"Submitted Version","type":"preprint","date_created":"2021-05-30T13:58:13Z","has_accepted_license":"1","oa":1,"title":"Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","_id":"9435","file":[{"relation":"main_file","content_type":"application/pdf","file_size":353431,"creator":"ekoudjin","file_id":"9436","checksum":"b281b5c2e3e90de0646c3eafcb2c6c25","access_level":"open_access","file_name":"CoExistence 2&3 caustics 3_17_6_2_3.pdf","date_updated":"2021-05-30T13:57:37Z","date_created":"2021-05-30T13:57:37Z"}],"author":[{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"orcid":"0000-0003-2640-4049","first_name":"Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","last_name":"Koudjinan","full_name":"Koudjinan, Edmond"}],"year":"2021","abstract":[{"lang":"eng","text":"For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries)."}],"date_updated":"2021-06-01T09:10:22Z"},{"quality_controlled":"1","volume":208,"intvolume":"       208","citation":{"ama":"Kaloshin V, Zhang K. <i>Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom</i>. Vol 208. 1st ed. Princeton University Press; 2020. doi:<a href=\"https://doi.org/10.1515/9780691204932\">10.1515/9780691204932</a>","ieee":"V. Kaloshin and K. Zhang, <i>Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom</i>, 1st ed., vol. 208. Princeton University Press, 2020.","short":"V. Kaloshin, K. Zhang, Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom, 1st ed., Princeton University Press, 2020.","ista":"Kaloshin V, Zhang K. 2020. Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom 1st ed., Princeton University Press, 224p.","mla":"Kaloshin, Vadim, and Ke Zhang. <i>Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom</i>. 1st ed., vol. 208, Princeton University Press, 2020, doi:<a href=\"https://doi.org/10.1515/9780691204932\">10.1515/9780691204932</a>.","apa":"Kaloshin, V., &#38; Zhang, K. (2020). <i>Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom</i> (1st ed., Vol. 208). Princeton University Press. <a href=\"https://doi.org/10.1515/9780691204932\">https://doi.org/10.1515/9780691204932</a>","chicago":"Kaloshin, Vadim, and Ke Zhang. <i>Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom</i>. 1st ed. Vol. 208. AMS. Princeton University Press, 2020. <a href=\"https://doi.org/10.1515/9780691204932\">https://doi.org/10.1515/9780691204932</a>."},"article_processing_charge":"No","scopus_import":"1","date_published":"2020-03-01T00:00:00Z","language":[{"iso":"eng"}],"oa_version":"None","type":"book","page":"224","date_created":"2020-09-17T10:41:05Z","doi":"10.1515/9780691204932","publication_status":"published","series_title":"AMS","alternative_title":["Annals of Mathematics Studies"],"month":"03","publication_identifier":{"isbn":["9-780-6912-0253-2"]},"title":"Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publisher":"Princeton University Press","status":"public","edition":"1","_id":"8414","author":[{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"first_name":"Ke","last_name":"Zhang","full_name":"Zhang, Ke"}],"year":"2020","extern":"1","day":"01","abstract":[{"text":"Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom).\r\nThis proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather’s strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.","lang":"eng"}],"date_updated":"2021-12-21T10:50:49Z"},{"status":"public","publication_identifier":{"issn":["0010-3616","1432-0916"]},"oa":1,"month":"05","date_updated":"2021-01-12T08:19:08Z","abstract":[{"lang":"eng","text":"We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift on three symbols that provides a natural labeling of all periodic orbits. We study the following inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of periodic orbits together with their labeling), determine the geometry of the billiard table? We show that from the Marked Length Spectrum it is possible to recover the curvature at periodic points of period two, as well as the Lyapunov exponent of each periodic orbit."}],"arxiv":1,"issue":"3","year":"2019","_id":"8415","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.08947"}],"intvolume":"       374","citation":{"ama":"Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical Physics</i>. 2019;374(3):1531-1575. doi:<a href=\"https://doi.org/10.1007/s00220-019-03448-x\">10.1007/s00220-019-03448-x</a>","ieee":"P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards,” <i>Communications in Mathematical Physics</i>, vol. 374, no. 3. Springer Nature, pp. 1531–1575, 2019.","short":"P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575.","chicago":"Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03448-x\">https://doi.org/10.1007/s00220-019-03448-x</a>.","mla":"Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:<a href=\"https://doi.org/10.1007/s00220-019-03448-x\">10.1007/s00220-019-03448-x</a>.","apa":"Bálint, P., De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2019). Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03448-x\">https://doi.org/10.1007/s00220-019-03448-x</a>","ista":"Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 374(3), 1531–1575."},"publication_status":"published","doi":"10.1007/s00220-019-03448-x","oa_version":"Preprint","date_published":"2019-05-09T00:00:00Z","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards","day":"09","extern":"1","author":[{"first_name":"Péter","last_name":"Bálint","full_name":"Bálint, Péter"},{"first_name":"Jacopo","last_name":"De Simoi","full_name":"De Simoi, Jacopo"},{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"full_name":"Leguil, Martin","first_name":"Martin","last_name":"Leguil"}],"article_processing_charge":"No","article_type":"original","external_id":{"arxiv":["1809.08947"]},"quality_controlled":"1","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"volume":374,"date_created":"2020-09-17T10:41:27Z","page":"1531-1575","publication":"Communications in Mathematical Physics","type":"journal_article","language":[{"iso":"eng"}]},{"publication_status":"published","doi":"10.17323/1609-4514-2019-19-2-307-327","oa_version":"Preprint","date_published":"2019-04-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1809.09341","open_access":"1"}],"citation":{"mla":"Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable Deformations of Strictly Convex Integrable Billiard Tables.” <i>Moscow Mathematical Journal</i>, vol. 19, no. 2, American Mathematical Society, 2019, pp. 307–27, doi:<a href=\"https://doi.org/10.17323/1609-4514-2019-19-2-307-327\">10.17323/1609-4514-2019-19-2-307-327</a>.","ista":"Huang G, Kaloshin V. 2019. On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables. Moscow Mathematical Journal. 19(2), 307–327.","apa":"Huang, G., &#38; Kaloshin, V. (2019). On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables. <i>Moscow Mathematical Journal</i>. American Mathematical Society. <a href=\"https://doi.org/10.17323/1609-4514-2019-19-2-307-327\">https://doi.org/10.17323/1609-4514-2019-19-2-307-327</a>","chicago":"Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable Deformations of Strictly Convex Integrable Billiard Tables.” <i>Moscow Mathematical Journal</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.17323/1609-4514-2019-19-2-307-327\">https://doi.org/10.17323/1609-4514-2019-19-2-307-327</a>.","short":"G. Huang, V. Kaloshin, Moscow Mathematical Journal 19 (2019) 307–327.","ama":"Huang G, Kaloshin V. On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables. <i>Moscow Mathematical Journal</i>. 2019;19(2):307-327. doi:<a href=\"https://doi.org/10.17323/1609-4514-2019-19-2-307-327\">10.17323/1609-4514-2019-19-2-307-327</a>","ieee":"G. Huang and V. Kaloshin, “On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables,” <i>Moscow Mathematical Journal</i>, vol. 19, no. 2. American Mathematical Society, pp. 307–327, 2019."},"intvolume":"        19","date_updated":"2021-01-12T08:19:08Z","issue":"2","abstract":[{"lang":"eng","text":"In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω0 preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω0."}],"arxiv":1,"year":"2019","_id":"8416","status":"public","publication_identifier":{"issn":["1609-4514"]},"oa":1,"month":"04","date_created":"2020-09-17T10:41:36Z","page":"307-327","publication":"Moscow Mathematical Journal","type":"journal_article","language":[{"iso":"eng"}],"article_type":"original","article_processing_charge":"No","external_id":{"arxiv":["1809.09341"]},"quality_controlled":"1","volume":19,"day":"01","extern":"1","author":[{"full_name":"Huang, Guan","last_name":"Huang","first_name":"Guan"},{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"}],"publisher":"American Mathematical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables"},{"article_type":"original","article_processing_charge":"No","keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"volume":233,"quality_controlled":"1","publication":"Archive for Rational Mechanics and Analysis","page":"799-836","date_created":"2020-09-17T10:41:51Z","type":"journal_article","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem","extern":"1","day":"12","author":[{"last_name":"Guardia","first_name":"Marcel","full_name":"Guardia, Marcel"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim"},{"full_name":"Zhang, Jianlu","last_name":"Zhang","first_name":"Jianlu"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00205-019-01368-7"}],"citation":{"ama":"Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. <i>Archive for Rational Mechanics and Analysis</i>. 2019;233(2):799-836. doi:<a href=\"https://doi.org/10.1007/s00205-019-01368-7\">10.1007/s00205-019-01368-7</a>","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019.","short":"M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis 233 (2019) 799–836.","mla":"Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:<a href=\"https://doi.org/10.1007/s00205-019-01368-7\">10.1007/s00205-019-01368-7</a>.","ista":"Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 233(2), 799–836.","apa":"Guardia, M., Kaloshin, V., &#38; Zhang, J. (2019). Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-019-01368-7\">https://doi.org/10.1007/s00205-019-01368-7</a>","chicago":"Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00205-019-01368-7\">https://doi.org/10.1007/s00205-019-01368-7</a>."},"intvolume":"       233","doi":"10.1007/s00205-019-01368-7","publication_status":"published","oa_version":"Published Version","date_published":"2019-03-12T00:00:00Z","status":"public","publication_identifier":{"issn":["0003-9527","1432-0673"]},"oa":1,"month":"03","issue":"2","abstract":[{"lang":"eng","text":"For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0."}],"date_updated":"2021-01-12T08:19:09Z","year":"2019","_id":"8418"},{"language":[{"iso":"eng"}],"date_published":"2018-09-05T00:00:00Z","oa_version":"None","type":"journal_article","page":"1173-1228","date_created":"2020-09-17T10:41:43Z","publication":"Communications in Mathematical Physics","publication_status":"published","doi":"10.1007/s00220-018-3248-z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"intvolume":"       366","citation":{"ieee":"A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability in the restricted planar elliptic three body problem,” <i>Communications in Mathematical Physics</i>, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.","ama":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted planar elliptic three body problem. <i>Communications in Mathematical Physics</i>. 2018;366(3):1173-1228. doi:<a href=\"https://doi.org/10.1007/s00220-018-3248-z\">10.1007/s00220-018-3248-z</a>","short":"A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical Physics 366 (2018) 1173–1228.","apa":"Delshams, A., Kaloshin, V., de la Rosa, A., &#38; Seara, T. M. (2018). Global instability in the restricted planar elliptic three body problem. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-018-3248-z\">https://doi.org/10.1007/s00220-018-3248-z</a>","mla":"Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” <i>Communications in Mathematical Physics</i>, vol. 366, no. 3, Springer Nature, 2018, pp. 1173–228, doi:<a href=\"https://doi.org/10.1007/s00220-018-3248-z\">10.1007/s00220-018-3248-z</a>.","ista":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 366(3), 1173–1228.","chicago":"Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00220-018-3248-z\">https://doi.org/10.1007/s00220-018-3248-z</a>."},"quality_controlled":"1","volume":366,"article_processing_charge":"No","article_type":"original","_id":"8417","author":[{"first_name":"Amadeu","last_name":"Delshams","full_name":"Delshams, Amadeu"},{"first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"de la Rosa, Abraham","first_name":"Abraham","last_name":"de la Rosa"},{"first_name":"Tere M.","last_name":"Seara","full_name":"Seara, Tere M."}],"day":"05","extern":"1","year":"2018","date_updated":"2021-01-12T08:19:08Z","abstract":[{"lang":"eng","text":"The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show the existence of orbits whose angular momentum performs arbitrary excursions in a large region. In particular, there exist diffusive orbits, that is, with a large variation of angular momentum. The leading idea of the proof consists in analyzing parabolic motions of the comet. By a well-known result of McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold at parabolic infinity. On P∞ it is possible to define two scattering maps, which contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic both in the future and the past. Since the inner dynamics inside P∞ is trivial, two different scattering maps are used. The combination of these two scattering maps permits the design of the desired diffusive pseudo-orbits. Using shadowing techniques and these pseudo orbits we show the existence of true trajectories of the RPETBP whose angular momentum varies in any predetermined fashion."}],"issue":"3","month":"09","title":"Global instability in the restricted planar elliptic three body problem","publication_identifier":{"issn":["0010-3616","1432-0916"]},"status":"public","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"oa_version":"None","type":"journal_article","language":[{"iso":"eng"}],"date_published":"2018-10-28T00:00:00Z","publication_status":"published","doi":"10.1098/rsta.2017.0419","date_created":"2020-09-17T10:42:01Z","publication":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":376,"citation":{"chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society, 2018. <a href=\"https://doi.org/10.1098/rsta.2017.0419\">https://doi.org/10.1098/rsta.2017.0419</a>.","mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 376, no. 2131, 20170419, The Royal Society, 2018, doi:<a href=\"https://doi.org/10.1098/rsta.2017.0419\">10.1098/rsta.2017.0419</a>.","ista":"Kaloshin V, Sorrentino A. 2018. On the integrability of Birkhoff billiards. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376(2131), 20170419.","apa":"Kaloshin, V., &#38; Sorrentino, A. (2018). On the integrability of Birkhoff billiards. <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rsta.2017.0419\">https://doi.org/10.1098/rsta.2017.0419</a>","ieee":"V. Kaloshin and A. Sorrentino, “On the integrability of Birkhoff billiards,” <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 376, no. 2131. The Royal Society, 2018.","ama":"Kaloshin V, Sorrentino A. On the integrability of Birkhoff billiards. <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2018;376(2131). doi:<a href=\"https://doi.org/10.1098/rsta.2017.0419\">10.1098/rsta.2017.0419</a>","short":"V. Kaloshin, A. Sorrentino, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2018)."},"keyword":["General Engineering","General Physics and Astronomy","General Mathematics"],"quality_controlled":"1","intvolume":"       376","article_type":"original","article_processing_charge":"No","article_number":"20170419","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim"},{"first_name":"Alfonso","last_name":"Sorrentino","full_name":"Sorrentino, Alfonso"}],"_id":"8419","date_updated":"2021-01-12T08:19:09Z","issue":"2131","abstract":[{"text":"In this survey, we provide a concise introduction to convex billiards and describe some recent results, obtained by the authors and collaborators, on the classification of integrable billiards, namely the so-called Birkhoff conjecture.\r\n\r\nThis article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.","lang":"eng"}],"day":"28","extern":"1","year":"2018","month":"10","status":"public","publisher":"The Royal Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the integrability of Birkhoff billiards","publication_identifier":{"issn":["1364-503X","1471-2962"]}},{"author":[{"full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"last_name":"Zhang","first_name":"Ke","full_name":"Zhang, Ke"}],"extern":"1","day":"15","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"IOP Publishing","title":"Density of convex billiards with rational caustics","type":"journal_article","language":[{"iso":"eng"}],"publication":"Nonlinearity","date_created":"2020-09-17T10:42:09Z","page":"5214-5234","volume":31,"keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"quality_controlled":"1","external_id":{"arxiv":["1706.07968"]},"article_processing_charge":"No","article_type":"original","_id":"8420","abstract":[{"lang":"eng","text":"We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number 1/q is polynomially sense in the smooth case, and exponentially dense in the analytic case."}],"arxiv":1,"issue":"11","date_updated":"2021-01-12T08:19:10Z","year":"2018","month":"10","status":"public","publication_identifier":{"issn":["0951-7715","1361-6544"]},"oa":1,"oa_version":"Preprint","date_published":"2018-10-15T00:00:00Z","doi":"10.1088/1361-6544/aadc12","publication_status":"published","intvolume":"        31","citation":{"ieee":"V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,” <i>Nonlinearity</i>, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.","ama":"Kaloshin V, Zhang K. Density of convex billiards with rational caustics. <i>Nonlinearity</i>. 2018;31(11):5214-5234. doi:<a href=\"https://doi.org/10.1088/1361-6544/aadc12\">10.1088/1361-6544/aadc12</a>","short":"V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.","mla":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” <i>Nonlinearity</i>, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:<a href=\"https://doi.org/10.1088/1361-6544/aadc12\">10.1088/1361-6544/aadc12</a>.","ista":"Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.","apa":"Kaloshin, V., &#38; Zhang, K. (2018). Density of convex billiards with rational caustics. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/aadc12\">https://doi.org/10.1088/1361-6544/aadc12</a>","chicago":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” <i>Nonlinearity</i>. IOP Publishing, 2018. <a href=\"https://doi.org/10.1088/1361-6544/aadc12\">https://doi.org/10.1088/1361-6544/aadc12</a>."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.07968"}]},{"article_type":"original","article_processing_charge":"No","quality_controlled":"1","volume":188,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"external_id":{"arxiv":["1612.09194"]},"publication":"Annals of Mathematics","date_created":"2020-09-17T10:42:22Z","page":"315-380","language":[{"iso":"eng"}],"type":"journal_article","title":"On the local Birkhoff conjecture for convex billiards","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Annals of Mathematics, Princeton U","extern":"1","day":"01","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"first_name":"Alfonso","last_name":"Sorrentino","full_name":"Sorrentino, Alfonso"}],"main_file_link":[{"url":"https://arxiv.org/abs/1612.09194","open_access":"1"}],"citation":{"short":"V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.","ieee":"V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex billiards,” <i>Annals of Mathematics</i>, vol. 188, no. 1. Annals of Mathematics, Princeton U, pp. 315–380, 2018.","ama":"Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. 2018;188(1):315-380. doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>","apa":"Kaloshin, V., &#38; Sorrentino, A. (2018). On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>","ista":"Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex billiards. Annals of Mathematics. 188(1), 315–380.","mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>, vol. 188, no. 1, Annals of Mathematics, Princeton U, 2018, pp. 315–80, doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>.","chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U, 2018. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>."},"intvolume":"       188","doi":"10.4007/annals.2018.188.1.6","publication_status":"published","date_published":"2018-07-01T00:00:00Z","oa_version":"Preprint","publication_identifier":{"issn":["0003-486X"]},"oa":1,"status":"public","month":"07","year":"2018","issue":"1","abstract":[{"text":"The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends and completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards into complex domains (with respect to the angle), and to thoroughly analyze the nature of their complex singularities. As an application, we are able to prove some spectral rigidity results for elliptic domains.","lang":"eng"}],"arxiv":1,"date_updated":"2021-01-12T08:19:10Z","_id":"8421"},{"year":"2018","date_updated":"2021-01-12T08:19:11Z","arxiv":1,"abstract":[{"lang":"eng","text":"The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of an ellipse of small eccentricity which preserves integrability near the boundary, is itself an ellipse. This extends the result in Avila et al. (Ann Math 184:527–558, ADK16), where integrability was assumed on a larger set. In particular, it shows that (local) integrability near the boundary implies global integrability. One of the crucial ideas in the proof consists in analyzing Taylor expansion of the corresponding action-angle coordinates with respect to the eccentricity parameter, deriving and studying higher order conditions for the preservation of integrable rational caustics."}],"issue":"2","_id":"8422","publication_identifier":{"issn":["1016-443X","1420-8970"]},"oa":1,"status":"public","month":"03","publication_status":"published","doi":"10.1007/s00039-018-0440-4","date_published":"2018-03-18T00:00:00Z","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.10601"}],"intvolume":"        28","citation":{"chicago":"Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “Nearly Circular Domains Which Are Integrable Close to the Boundary Are Ellipses.” <i>Geometric and Functional Analysis</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00039-018-0440-4\">https://doi.org/10.1007/s00039-018-0440-4</a>.","apa":"Huang, G., Kaloshin, V., &#38; Sorrentino, A. (2018). Nearly circular domains which are integrable close to the boundary are ellipses. <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-018-0440-4\">https://doi.org/10.1007/s00039-018-0440-4</a>","ista":"Huang G, Kaloshin V, Sorrentino A. 2018. Nearly circular domains which are integrable close to the boundary are ellipses. Geometric and Functional Analysis. 28(2), 334–392.","mla":"Huang, Guan, et al. “Nearly Circular Domains Which Are Integrable Close to the Boundary Are Ellipses.” <i>Geometric and Functional Analysis</i>, vol. 28, no. 2, Springer Nature, 2018, pp. 334–92, doi:<a href=\"https://doi.org/10.1007/s00039-018-0440-4\">10.1007/s00039-018-0440-4</a>.","ama":"Huang G, Kaloshin V, Sorrentino A. Nearly circular domains which are integrable close to the boundary are ellipses. <i>Geometric and Functional Analysis</i>. 2018;28(2):334-392. doi:<a href=\"https://doi.org/10.1007/s00039-018-0440-4\">10.1007/s00039-018-0440-4</a>","ieee":"G. Huang, V. Kaloshin, and A. Sorrentino, “Nearly circular domains which are integrable close to the boundary are ellipses,” <i>Geometric and Functional Analysis</i>, vol. 28, no. 2. Springer Nature, pp. 334–392, 2018.","short":"G. Huang, V. Kaloshin, A. Sorrentino, Geometric and Functional Analysis 28 (2018) 334–392."},"day":"18","extern":"1","author":[{"last_name":"Huang","first_name":"Guan","full_name":"Huang, Guan"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"full_name":"Sorrentino, Alfonso","first_name":"Alfonso","last_name":"Sorrentino"}],"title":"Nearly circular domains which are integrable close to the boundary are ellipses","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-09-17T10:42:30Z","page":"334-392","publication":"Geometric and Functional Analysis","language":[{"iso":"eng"}],"type":"journal_article","article_processing_charge":"No","article_type":"original","external_id":{"arxiv":["1705.10601"]},"quality_controlled":"1","volume":28,"keyword":["Geometry and Topology","Analysis"]},{"doi":"10.1134/s1560354718010057","publication_status":"published","oa_version":"Preprint","date_published":"2018-02-05T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1801.00952","open_access":"1"}],"citation":{"chicago":"Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.” <i>Regular and Chaotic Dynamics</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1134/s1560354718010057\">https://doi.org/10.1134/s1560354718010057</a>.","mla":"Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.” <i>Regular and Chaotic Dynamics</i>, vol. 23, Springer Nature, 2018, pp. 54–59, doi:<a href=\"https://doi.org/10.1134/s1560354718010057\">10.1134/s1560354718010057</a>.","ista":"Buhovsky L, Kaloshin V. 2018. Nonisometric domains with the same Marvizi-Melrose invariants. Regular and Chaotic Dynamics. 23, 54–59.","apa":"Buhovsky, L., &#38; Kaloshin, V. (2018). Nonisometric domains with the same Marvizi-Melrose invariants. <i>Regular and Chaotic Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/s1560354718010057\">https://doi.org/10.1134/s1560354718010057</a>","short":"L. Buhovsky, V. Kaloshin, Regular and Chaotic Dynamics 23 (2018) 54–59.","ama":"Buhovsky L, Kaloshin V. Nonisometric domains with the same Marvizi-Melrose invariants. <i>Regular and Chaotic Dynamics</i>. 2018;23:54-59. doi:<a href=\"https://doi.org/10.1134/s1560354718010057\">10.1134/s1560354718010057</a>","ieee":"L. Buhovsky and V. Kaloshin, “Nonisometric domains with the same Marvizi-Melrose invariants,” <i>Regular and Chaotic Dynamics</i>, vol. 23. Springer Nature, pp. 54–59, 2018."},"intvolume":"        23","arxiv":1,"abstract":[{"lang":"eng","text":"For any strictly convex planar domain Ω ⊂ R2 with a C∞ boundary one can associate an infinite sequence of spectral invariants introduced by Marvizi–Merlose [5]. These invariants can generically be determined using the spectrum of the Dirichlet problem of the Laplace operator. A natural question asks if this collection is sufficient to determine Ω up to isometry. In this paper we give a counterexample, namely, we present two nonisometric domains Ω and Ω¯ with the same collection of Marvizi–Melrose invariants. Moreover, each domain has countably many periodic orbits {Sn}n≥1 (resp. {S¯n}n⩾1) of period going to infinity such that Sn and S¯n have the same period and perimeter for each n."}],"date_updated":"2021-01-12T08:19:11Z","year":"2018","_id":"8426","status":"public","oa":1,"publication_identifier":{"issn":["1560-3547","1468-4845"]},"month":"02","publication":"Regular and Chaotic Dynamics","page":"54-59","date_created":"2020-09-17T10:43:21Z","type":"journal_article","language":[{"iso":"eng"}],"article_processing_charge":"No","article_type":"original","quality_controlled":"1","volume":23,"external_id":{"arxiv":["1801.00952"]},"extern":"1","day":"05","author":[{"last_name":"Buhovsky","first_name":"Lev","full_name":"Buhovsky, Lev"},{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Nonisometric domains with the same Marvizi-Melrose invariants"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1603.08838"}],"intvolume":"       167","citation":{"ieee":"G. Huang, V. Kaloshin, and A. Sorrentino, “On the marked length spectrum of generic strictly convex billiard tables,” <i>Duke Mathematical Journal</i>, vol. 167, no. 1. Duke University Press, pp. 175–209, 2017.","ama":"Huang G, Kaloshin V, Sorrentino A. On the marked length spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>. 2017;167(1):175-209. doi:<a href=\"https://doi.org/10.1215/00127094-2017-0038\">10.1215/00127094-2017-0038</a>","short":"G. Huang, V. Kaloshin, A. Sorrentino, Duke Mathematical Journal 167 (2017) 175–209.","chicago":"Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>. Duke University Press, 2017. <a href=\"https://doi.org/10.1215/00127094-2017-0038\">https://doi.org/10.1215/00127094-2017-0038</a>.","mla":"Huang, Guan, et al. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>, vol. 167, no. 1, Duke University Press, 2017, pp. 175–209, doi:<a href=\"https://doi.org/10.1215/00127094-2017-0038\">10.1215/00127094-2017-0038</a>.","ista":"Huang G, Kaloshin V, Sorrentino A. 2017. On the marked length spectrum of generic strictly convex billiard tables. Duke Mathematical Journal. 167(1), 175–209.","apa":"Huang, G., Kaloshin, V., &#38; Sorrentino, A. (2017). On the marked length spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2017-0038\">https://doi.org/10.1215/00127094-2017-0038</a>"},"doi":"10.1215/00127094-2017-0038","publication_status":"published","date_published":"2017-12-08T00:00:00Z","oa_version":"Preprint","publication_identifier":{"issn":["0012-7094"]},"oa":1,"status":"public","month":"12","year":"2017","issue":"1","arxiv":1,"abstract":[{"text":"In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard map from the (maximal) marked length spectrum of the domain.","lang":"eng"}],"date_updated":"2021-01-12T08:19:11Z","_id":"8423","article_processing_charge":"No","article_type":"original","volume":167,"quality_controlled":"1","external_id":{"arxiv":["1603.08838"]},"publication":"Duke Mathematical Journal","page":"175-209","date_created":"2020-09-17T10:42:42Z","language":[{"iso":"eng"}],"type":"journal_article","title":"On the marked length spectrum of generic strictly convex billiard tables","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Duke University Press","extern":"1","day":"08","author":[{"last_name":"Huang","first_name":"Guan","full_name":"Huang, Guan"},{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Sorrentino","first_name":"Alfonso","full_name":"Sorrentino, Alfonso"}]},{"title":"Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Annals of Mathematics","extern":"1","day":"01","author":[{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"Wei, Qiaoling","first_name":"Qiaoling","last_name":"Wei"}],"article_type":"original","article_processing_charge":"No","volume":186,"quality_controlled":"1","external_id":{"arxiv":["1606.00230"]},"publication":"Annals of Mathematics","date_created":"2020-09-17T10:46:42Z","page":"277-314","language":[{"iso":"eng"}],"type":"journal_article","oa":1,"publication_identifier":{"issn":["0003-486X"]},"status":"public","month":"07","year":"2017","abstract":[{"lang":"eng","text":"We show that any sufficiently (finitely) smooth ℤ₂-symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all deformations among domains in the same class that preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak."}],"issue":"1","arxiv":1,"date_updated":"2021-01-12T08:19:12Z","_id":"8427","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.00230"}],"citation":{"ama":"De Simoi J, Kaloshin V, Wei Q. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. <i>Annals of Mathematics</i>. 2017;186(1):277-314. doi:<a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">10.4007/annals.2017.186.1.7</a>","ieee":"J. De Simoi, V. Kaloshin, and Q. Wei, “Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle,” <i>Annals of Mathematics</i>, vol. 186, no. 1. Annals of Mathematics, pp. 277–314, 2017.","short":"J. De Simoi, V. Kaloshin, Q. Wei, Annals of Mathematics 186 (2017) 277–314.","mla":"De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” <i>Annals of Mathematics</i>, vol. 186, no. 1, Annals of Mathematics, 2017, pp. 277–314, doi:<a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">10.4007/annals.2017.186.1.7</a>.","apa":"De Simoi, J., Kaloshin, V., &#38; Wei, Q. (2017). Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. <i>Annals of Mathematics</i>. Annals of Mathematics. <a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">https://doi.org/10.4007/annals.2017.186.1.7</a>","ista":"De Simoi J, Kaloshin V, Wei Q. 2017. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. Annals of Mathematics. 186(1), 277–314.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Qiaoling Wei. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” <i>Annals of Mathematics</i>. Annals of Mathematics, 2017. <a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">https://doi.org/10.4007/annals.2017.186.1.7</a>."},"intvolume":"       186","doi":"10.4007/annals.2017.186.1.7","publication_status":"published","date_published":"2017-07-01T00:00:00Z","oa_version":"Preprint"},{"_id":"8493","author":[{"full_name":"Guardia, M.","first_name":"M.","last_name":"Guardia"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"first_name":"J.","last_name":"Zhang","full_name":"Zhang, J."}],"year":"2016","extern":"1","day":"01","abstract":[{"text":"In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.","lang":"eng"}],"date_updated":"2021-01-12T08:19:39Z","month":"11","publication_identifier":{"issn":["0010-3616","1432-0916"]},"title":"A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publisher":"Springer Nature","date_published":"2016-11-01T00:00:00Z","language":[{"iso":"eng"}],"oa_version":"None","type":"journal_article","publication":"Communications in Mathematical Physics","date_created":"2020-09-18T10:45:50Z","page":"321-361","doi":"10.1007/s00220-016-2705-9","publication_status":"published","citation":{"short":"M. Guardia, V. Kaloshin, J. Zhang, Communications in Mathematical Physics 348 (2016) 321–361.","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems,” <i>Communications in Mathematical Physics</i>, vol. 348. Springer Nature, pp. 321–361, 2016.","ama":"Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. <i>Communications in Mathematical Physics</i>. 2016;348:321-361. doi:<a href=\"https://doi.org/10.1007/s00220-016-2705-9\">10.1007/s00220-016-2705-9</a>","mla":"Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” <i>Communications in Mathematical Physics</i>, vol. 348, Springer Nature, 2016, pp. 321–61, doi:<a href=\"https://doi.org/10.1007/s00220-016-2705-9\">10.1007/s00220-016-2705-9</a>.","ista":"Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 348, 321–361.","apa":"Guardia, M., Kaloshin, V., &#38; Zhang, J. (2016). A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-016-2705-9\">https://doi.org/10.1007/s00220-016-2705-9</a>","chicago":"Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2016. <a href=\"https://doi.org/10.1007/s00220-016-2705-9\">https://doi.org/10.1007/s00220-016-2705-9</a>."},"intvolume":"       348","quality_controlled":"1","volume":348,"article_type":"original","article_processing_charge":"No"},{"quality_controlled":"1","volume":217,"intvolume":"       217","citation":{"apa":"Bernard, P., Kaloshin, V., &#38; Zhang, K. (2016). Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. Institut Mittag-Leffler. <a href=\"https://doi.org/10.1007/s11511-016-0141-5\">https://doi.org/10.1007/s11511-016-0141-5</a>","mla":"Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>, vol. 217, no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:<a href=\"https://doi.org/10.1007/s11511-016-0141-5\">10.1007/s11511-016-0141-5</a>.","ista":"Bernard P, Kaloshin V, Zhang K. 2016. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. Acta Mathematica. 217(1), 1–79.","chicago":"Bernard, Patrick, Vadim Kaloshin, and Ke Zhang. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>. Institut Mittag-Leffler, 2016. <a href=\"https://doi.org/10.1007/s11511-016-0141-5\">https://doi.org/10.1007/s11511-016-0141-5</a>.","ieee":"P. Bernard, V. Kaloshin, and K. Zhang, “Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders,” <i>Acta Mathematica</i>, vol. 217, no. 1. Institut Mittag-Leffler, pp. 1–79, 2016.","ama":"Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. 2016;217(1):1-79. doi:<a href=\"https://doi.org/10.1007/s11511-016-0141-5\">10.1007/s11511-016-0141-5</a>","short":"P. Bernard, V. Kaloshin, K. Zhang, Acta Mathematica 217 (2016) 1–79."},"article_processing_charge":"No","article_type":"original","oa_version":"None","type":"journal_article","language":[{"iso":"eng"}],"date_published":"2016-09-28T00:00:00Z","publication_status":"published","doi":"10.1007/s11511-016-0141-5","date_created":"2020-09-18T10:46:07Z","page":"1-79","publication":"Acta Mathematica","month":"09","publisher":"Institut Mittag-Leffler","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders","publication_identifier":{"issn":["0001-5962"]},"author":[{"full_name":"Bernard, Patrick","first_name":"Patrick","last_name":"Bernard"},{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Zhang","first_name":"Ke","full_name":"Zhang, Ke"}],"_id":"8494","date_updated":"2021-01-12T08:19:39Z","abstract":[{"text":"We prove a form of Arnold diffusion in the a-priori stable case. Let\r\nH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\r\nbe a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying\r\n∥p(t)−p(0)∥>l(H1)>0,\r\nwhere l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.\r\n\r\nFor the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.","lang":"eng"}],"issue":"1","day":"28","year":"2016","extern":"1"},{"publication":"Annals of Mathematics","date_created":"2020-09-18T10:46:22Z","page":"527-558","doi":"10.4007/annals.2016.184.2.5","publication_status":"published","date_published":"2016-09-01T00:00:00Z","language":[{"iso":"eng"}],"type":"journal_article","oa_version":"None","article_processing_charge":"No","article_type":"original","volume":184,"quality_controlled":"1","intvolume":"       184","citation":{"chicago":"Avila, Artur, Jacopo De Simoi, and Vadim Kaloshin. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.” <i>Annals of Mathematics</i>. Princeton University Press, 2016. <a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">https://doi.org/10.4007/annals.2016.184.2.5</a>.","mla":"Avila, Artur, et al. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.” <i>Annals of Mathematics</i>, vol. 184, no. 2, Princeton University Press, 2016, pp. 527–58, doi:<a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">10.4007/annals.2016.184.2.5</a>.","ista":"Avila A, De Simoi J, Kaloshin V. 2016. An integrable deformation of an ellipse of small eccentricity is an ellipse. Annals of Mathematics. 184(2), 527–558.","apa":"Avila, A., De Simoi, J., &#38; Kaloshin, V. (2016). An integrable deformation of an ellipse of small eccentricity is an ellipse. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">https://doi.org/10.4007/annals.2016.184.2.5</a>","ama":"Avila A, De Simoi J, Kaloshin V. An integrable deformation of an ellipse of small eccentricity is an ellipse. <i>Annals of Mathematics</i>. 2016;184(2):527-558. doi:<a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">10.4007/annals.2016.184.2.5</a>","ieee":"A. Avila, J. De Simoi, and V. Kaloshin, “An integrable deformation of an ellipse of small eccentricity is an ellipse,” <i>Annals of Mathematics</i>, vol. 184, no. 2. Princeton University Press, pp. 527–558, 2016.","short":"A. Avila, J. De Simoi, V. Kaloshin, Annals of Mathematics 184 (2016) 527–558."},"year":"2016","extern":"1","day":"01","issue":"2","date_updated":"2021-01-12T08:19:40Z","_id":"8496","author":[{"full_name":"Avila, Artur","first_name":"Artur","last_name":"Avila"},{"full_name":"De Simoi, Jacopo","first_name":"Jacopo","last_name":"De Simoi"},{"first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"}],"publication_identifier":{"issn":["0003-486X"]},"title":"An integrable deformation of an ellipse of small eccentricity is an ellipse","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publisher":"Princeton University Press","month":"09"},{"article_type":"original","article_processing_charge":"No","intvolume":"        18","citation":{"chicago":"Féjoz, Jacques, Marcel Guàrdia, Vadim Kaloshin, and Pablo Roldán. “Kirkwood Gaps and Diffusion along Mean Motion Resonances in the Restricted Planar Three-Body Problem.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House, 2016. <a href=\"https://doi.org/10.4171/jems/642\">https://doi.org/10.4171/jems/642</a>.","mla":"Féjoz, Jacques, et al. “Kirkwood Gaps and Diffusion along Mean Motion Resonances in the Restricted Planar Three-Body Problem.” <i>Journal of the European Mathematical Society</i>, vol. 18, no. 10, European Mathematical Society Publishing House, 2016, pp. 2315–403, doi:<a href=\"https://doi.org/10.4171/jems/642\">10.4171/jems/642</a>.","apa":"Féjoz, J., Guàrdia, M., Kaloshin, V., &#38; Roldán, P. (2016). Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House. <a href=\"https://doi.org/10.4171/jems/642\">https://doi.org/10.4171/jems/642</a>","ista":"Féjoz J, Guàrdia M, Kaloshin V, Roldán P. 2016. Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. Journal of the European Mathematical Society. 18(10), 2315–2403.","short":"J. Féjoz, M. Guàrdia, V. Kaloshin, P. Roldán, Journal of the European Mathematical Society 18 (2016) 2315–2403.","ieee":"J. Féjoz, M. Guàrdia, V. Kaloshin, and P. Roldán, “Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem,” <i>Journal of the European Mathematical Society</i>, vol. 18, no. 10. European Mathematical Society Publishing House, pp. 2315–2403, 2016.","ama":"Féjoz J, Guàrdia M, Kaloshin V, Roldán P. Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. <i>Journal of the European Mathematical Society</i>. 2016;18(10):2315-2403. doi:<a href=\"https://doi.org/10.4171/jems/642\">10.4171/jems/642</a>"},"quality_controlled":"1","volume":18,"publication":"Journal of the European Mathematical Society","page":"2315-2403","date_created":"2020-09-18T10:46:31Z","doi":"10.4171/jems/642","publication_status":"published","date_published":"2016-09-19T00:00:00Z","language":[{"iso":"eng"}],"oa_version":"None","type":"journal_article","publication_identifier":{"issn":["1435-9855"]},"title":"Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"European Mathematical Society Publishing House","status":"public","month":"09","extern":"1","year":"2016","day":"19","abstract":[{"lang":"eng","text":"We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun–Jupiter–asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio μ=10−3 and a small eccentricity e0>0. The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. In the proof we verify certain non-degeneracy conditions numerically.\r\n\r\nBased on the work of Treschev, it is natural to conjecture that the time of diffusion for this problem is ∼−ln(μe0)μ3/2e0. We expect our instability mechanism to apply to realistic values of e0 and we give heuristic arguments in its favor. If so, the applicability of Nekhoroshev theory to the three-body problem as well as the long time stability become questionable.\r\n\r\nIt is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. Our mechanism gives a possible explanation of their existence. To relate the existence of Kirkwood gaps with Arnol'd diffusion, we also state a conjecture on its existence for a typical ϵ-perturbation of the product of the pendulum and the rotator. Namely, we predict that a positive conditional measure of initial conditions concentrated in the main resonance exhibits Arnol’d diffusion on time scales −lnϵϵ2."}],"issue":"10","date_updated":"2021-01-12T08:19:41Z","_id":"8497","author":[{"first_name":"Jacques","last_name":"Féjoz","full_name":"Féjoz, Jacques"},{"full_name":"Guàrdia, Marcel","last_name":"Guàrdia","first_name":"Marcel"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"full_name":"Roldán, Pablo","last_name":"Roldán","first_name":"Pablo"}]}]