{"external_id":{"isi":["000865267300002"],"arxiv":["2105.14640"]},"publication_identifier":{"eissn":["1468-4845"],"issn":["1560-3547"]},"page":"525-537","doi":"10.1134/S1560354722050021","publication":"Regular and Chaotic Dynamics","author":[{"full_name":"Koudjinan, Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","last_name":"Koudjinan","first_name":"Edmond","orcid":"0000-0003-2640-4049"},{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"}],"language":[{"iso":"eng"}],"_id":"12145","ec_funded":1,"article_type":"original","citation":{"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>.","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.","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>.","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>","ista":"Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537.","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>","short":"E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537."},"year":"2022","intvolume":"        27","volume":27,"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020"}],"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).","isi":1,"keyword":["Mechanical Engineering","Applied Mathematics","Mathematical Physics","Modeling and Simulation","Statistical and Nonlinear Physics","Mathematics (miscellaneous)"],"article_processing_charge":"No","month":"10","date_updated":"2023-08-04T08:59:14Z","type":"journal_article","day":"03","department":[{"_id":"VaKa"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.14640","open_access":"1"}],"abstract":[{"lang":"eng","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."}],"date_published":"2022-10-03T00:00:00Z","publication_status":"published","issue":"6","publisher":"Springer Nature","scopus_import":"1","oa":1,"oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2023-01-12T12:06:49Z","quality_controlled":"1","title":"On some invariants of Birkhoff billiards under conjugacy","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1134/s1560354722060107"}]},"status":"public"}