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