[{"file":[{"content_type":"application/pdf","relation":"main_file","file_id":"9990","creator":"cchlebak","file_name":"2021_CommunMathPhys_Wirth.pdf","file_size":505971,"date_created":"2021-09-08T07:34:24Z","checksum":"8a602f916b1c2b0dc1159708b7cb204b","date_updated":"2021-09-08T09:46:34Z","access_level":"open_access"}],"date_created":"2021-08-30T10:07:44Z","department":[{"_id":"JaMa"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","article_type":"original","date_published":"2021-08-30T00:00:00Z","month":"08","file_date_updated":"2021-09-08T09:46:34Z","page":"761–791","publication":"Communications in Mathematical Physics","status":"public","intvolume":"       387","type":"journal_article","day":"30","ddc":["621"],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"title":"Complete gradient estimates of quantum Markov semigroups","external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"ec_funded":1,"doi":"10.1007/s00220-021-04199-4","year":"2021","quality_controlled":"1","oa_version":"Published Version","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"_id":"9973","article_processing_charge":"Yes (via OA deal)","oa":1,"volume":387,"date_updated":"2023-08-11T11:09:07Z","arxiv":1,"author":[{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth","first_name":"Melchior"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"abstract":[{"lang":"eng","text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors."}],"citation":{"apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021.","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>.","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791."},"publication_status":"published"},{"day":"09","type":"journal_article","intvolume":"       374","status":"public","publication":"Communications in Mathematical Physics","issue":"3","page":"1531-1575","month":"05","article_type":"original","date_published":"2019-05-09T00:00:00Z","publisher":"Springer Nature","language":[{"iso":"eng"}],"date_created":"2020-09-17T10:41:27Z","citation":{"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>.","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.","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>","short":"P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575.","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.","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>.","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>"},"publication_status":"published","abstract":[{"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.","lang":"eng"}],"author":[{"full_name":"Bálint, Péter","last_name":"Bálint","first_name":"Péter"},{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"Martin","last_name":"Leguil","full_name":"Leguil, Martin"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"arxiv":1,"article_processing_charge":"No","date_updated":"2021-01-12T08:19:08Z","volume":374,"oa":1,"extern":"1","publication_identifier":{"issn":["0010-3616","1432-0916"]},"_id":"8415","oa_version":"Preprint","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00220-019-03448-x","year":"2019","title":"Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards","external_id":{"arxiv":["1809.08947"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.08947"}]},{"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","author":[{"first_name":"Amadeu","full_name":"Delshams, Amadeu","last_name":"Delshams"},{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"Abraham","full_name":"de la Rosa, Abraham","last_name":"de la Rosa"},{"full_name":"Seara, Tere M.","last_name":"Seara","first_name":"Tere M."}],"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."}],"intvolume":"       366","type":"journal_article","day":"05","citation":{"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>","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.","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>.","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>","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.","short":"A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical Physics 366 (2018) 1173–1228."},"publication_status":"published","oa_version":"None","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0010-3616","1432-0916"]},"extern":"1","_id":"8417","page":"1173-1228","article_processing_charge":"No","volume":366,"date_updated":"2021-01-12T08:19:08Z","publication":"Communications in Mathematical Physics","issue":"3","language":[{"iso":"eng"}],"title":"Global instability in the restricted planar elliptic three body problem","publisher":"Springer Nature","article_type":"original","date_published":"2018-09-05T00:00:00Z","doi":"10.1007/s00220-018-3248-z","year":"2018","month":"09","date_created":"2020-09-17T10:41:43Z"},{"day":"15","type":"journal_article","intvolume":"        31","status":"public","issue":"11","publication":"Nonlinearity","page":"5214-5234","month":"10","article_type":"original","date_published":"2018-10-15T00:00:00Z","publisher":"IOP Publishing","language":[{"iso":"eng"}],"date_created":"2020-09-17T10:42:09Z","publication_status":"published","citation":{"ista":"Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.","short":"V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.","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>","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>.","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>.","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.","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>"},"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."}],"author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"first_name":"Ke","full_name":"Zhang, Ke","last_name":"Zhang"}],"keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"arxiv":1,"oa":1,"volume":31,"date_updated":"2021-01-12T08:19:10Z","article_processing_charge":"No","_id":"8420","publication_identifier":{"issn":["0951-7715","1361-6544"]},"extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"Preprint","doi":"10.1088/1361-6544/aadc12","year":"2018","title":"Density of convex billiards with rational caustics","external_id":{"arxiv":["1706.07968"]},"main_file_link":[{"url":"https://arxiv.org/abs/1706.07968","open_access":"1"}]},{"date_created":"2020-09-18T10:46:43Z","doi":"10.1088/0951-7715/28/8/2699","year":"2015","month":"06","date_published":"2015-06-30T00:00:00Z","article_type":"original","publisher":"IOP Publishing","title":"Arnold diffusion for smooth convex systems of two and a half degrees of freedom","language":[{"iso":"eng"}],"issue":"8","publication":"Nonlinearity","volume":28,"date_updated":"2021-01-12T08:19:41Z","page":"2699-2720","article_processing_charge":"No","_id":"8498","extern":"1","publication_identifier":{"issn":["0951-7715","1361-6544"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","quality_controlled":"1","publication_status":"published","citation":{"short":"V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720.","ista":"Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720.","ama":"Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. <i>Nonlinearity</i>. 2015;28(8):2699-2720. doi:<a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">10.1088/0951-7715/28/8/2699</a>","mla":"Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” <i>Nonlinearity</i>, vol. 28, no. 8, IOP Publishing, 2015, pp. 2699–720, doi:<a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">10.1088/0951-7715/28/8/2699</a>.","chicago":"Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” <i>Nonlinearity</i>. IOP Publishing, 2015. <a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">https://doi.org/10.1088/0951-7715/28/8/2699</a>.","apa":"Kaloshin, V., &#38; Zhang, K. (2015). Arnold diffusion for smooth convex systems of two and a half degrees of freedom. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">https://doi.org/10.1088/0951-7715/28/8/2699</a>","ieee":"V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two and a half degrees of freedom,” <i>Nonlinearity</i>, vol. 28, no. 8. IOP Publishing, pp. 2699–2720, 2015."},"day":"30","type":"journal_article","abstract":[{"lang":"eng","text":"In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$  be a 2-dimensional torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ > 0. Our main result says that for a 'generic' time-periodic perturbation of an integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad \\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a 'connected' net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7]."}],"intvolume":"        28","status":"public","author":[{"first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"K","last_name":"Zhang","full_name":"Zhang, K"}],"keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"]},{"date_created":"2020-09-18T10:47:16Z","year":"2012","month":"11","doi":"10.1007/s00220-012-1532-x","article_type":"original","date_published":"2012-11-01T00:00:00Z","publisher":"Springer Nature","title":"An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension","language":[{"iso":"eng"}],"issue":"3","publication":"Communications in Mathematical Physics","date_updated":"2021-01-12T08:19:44Z","volume":315,"page":"643-697","article_processing_charge":"No","_id":"8502","publication_identifier":{"issn":["0010-3616","1432-0916"]},"extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","quality_controlled":"1","publication_status":"published","day":"01","citation":{"chicago":"Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2012. <a href=\"https://doi.org/10.1007/s00220-012-1532-x\">https://doi.org/10.1007/s00220-012-1532-x</a>.","ieee":"V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension,” <i>Communications in Mathematical Physics</i>, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012.","apa":"Kaloshin, V., &#38; Saprykina, M. (2012). An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-012-1532-x\">https://doi.org/10.1007/s00220-012-1532-x</a>","short":"V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697.","ista":"Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 315(3), 643–697.","ama":"Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. <i>Communications in Mathematical Physics</i>. 2012;315(3):643-697. doi:<a href=\"https://doi.org/10.1007/s00220-012-1532-x\">10.1007/s00220-012-1532-x</a>","mla":"Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” <i>Communications in Mathematical Physics</i>, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97, doi:<a href=\"https://doi.org/10.1007/s00220-012-1532-x\">10.1007/s00220-012-1532-x</a>."},"type":"journal_article","abstract":[{"text":"The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface.","lang":"eng"}],"intvolume":"       315","status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"author":[{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Saprykina","full_name":"Saprykina, Maria","first_name":"Maria"}]},{"date_published":"2000-04-01T00:00:00Z","article_type":"original","year":"2000","doi":"10.1007/s002200050811","month":"04","language":[{"iso":"eng"}],"publisher":"Springer Nature","title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","date_created":"2020-09-18T10:50:20Z","type":"journal_article","publication_status":"published","citation":{"short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","mla":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>, vol. 211, Springer Nature, 2000, pp. 253–71, doi:<a href=\"https://doi.org/10.1007/s002200050811\">10.1007/s002200050811</a>.","ama":"Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. 2000;211:253-271. doi:<a href=\"https://doi.org/10.1007/s002200050811\">10.1007/s002200050811</a>","chicago":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2000. <a href=\"https://doi.org/10.1007/s002200050811\">https://doi.org/10.1007/s002200050811</a>.","apa":"Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s002200050811\">https://doi.org/10.1007/s002200050811</a>","ieee":"V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” <i>Communications in Mathematical Physics</i>, vol. 211. Springer Nature, pp. 253–271, 2000."},"day":"01","author":[{"first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"abstract":[{"lang":"eng","text":"Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented."}],"intvolume":"       211","volume":211,"date_updated":"2021-01-12T08:19:52Z","page":"253-271","article_processing_charge":"No","publication":"Communications in Mathematical Physics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"None","_id":"8525","extern":"1","publication_identifier":{"issn":["0010-3616","1432-0916"]}},{"publisher":"IOP Publishing","title":"How projections affect the dimension spectrum of fractal measures","language":[{"iso":"eng"}],"year":"1997","month":"06","doi":"10.1088/0951-7715/10/5/002","article_type":"original","date_published":"1997-06-19T00:00:00Z","date_created":"2020-09-18T10:50:41Z","intvolume":"        10","abstract":[{"text":"We introduce a new potential-theoretic definition of the dimension spectrum  of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if  and  is a Borel probability measure with compact support in , then under almost every linear transformation from  to , the q-dimension of the image of  is ; in particular, the q-dimension of  is preserved provided . We also present results on the preservation of information dimension  and pointwise dimension. Finally, for  and q > 2 we give examples for which  is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions.","lang":"eng"}],"keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"author":[{"first_name":"Brian R","last_name":"Hunt","full_name":"Hunt, Brian R"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"status":"public","publication_status":"published","day":"19","citation":{"ama":"Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. 1997;10(5):1031-1046. doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>","mla":"Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>.","ista":"Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046.","short":"B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.","apa":"Hunt, B. R., &#38; Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>","ieee":"B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” <i>Nonlinearity</i>, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997.","chicago":"Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>. IOP Publishing, 1997. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>."},"type":"journal_article","_id":"8527","publication_identifier":{"issn":["0951-7715","1361-6544"]},"extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"None","issue":"5","publication":"Nonlinearity","volume":10,"date_updated":"2021-01-12T08:19:53Z","article_processing_charge":"No","page":"1031-1046"}]