{"_id":"12877","page":"829-901","month":"08","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","ec_funded":1,"isi":1,"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-10-04T11:25:37Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1905.00890","open_access":"1"}],"oa":1,"abstract":[{"lang":"eng","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."}],"date_created":"2023-04-30T22:01:05Z","publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"intvolume":"       233","publisher":"Springer Nature","author":[{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"first_name":"Martin","last_name":"Leguil","full_name":"Leguil, Martin"}],"article_processing_charge":"No","external_id":{"isi":["000978887600001"],"arxiv":["1905.00890"]},"department":[{"_id":"VaKa"}],"title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","article_type":"original","doi":"10.1007/s00222-023-01191-8","project":[{"call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707"}],"oa_version":"Preprint","scopus_import":"1","status":"public","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.","year":"2023","publication":"Inventiones Mathematicae","type":"journal_article","volume":233,"date_published":"2023-08-01T00:00:00Z","citation":{"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>","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.","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>.","short":"J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023) 829–901.","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>.","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.","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>"}}