{"status":"public","article_type":"original","_id":"14427","ec_funded":1,"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","call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"oa_version":"Preprint","department":[{"_id":"VaKa"}],"doi":"10.1007/s00220-023-04837-z","date_updated":"2023-12-13T13:02:44Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Communications in Mathematical Physics","month":"09","date_created":"2023-10-15T22:01:11Z","publication_status":"epub_ahead","publisher":"Springer Nature","external_id":{"arxiv":["1902.07330"],"isi":["001073177200001"]},"date_published":"2023-09-29T00:00:00Z","quality_controlled":"1","scopus_import":"1","citation":{"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>.","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics.","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.","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>.","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>","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics (2023)."},"title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","article_processing_charge":"No","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"author":[{"full_name":"Chen, Jianyu","first_name":"Jianyu","last_name":"Chen"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"Zhang, Hong Kun","last_name":"Zhang","first_name":"Hong Kun"}],"language":[{"iso":"eng"}],"day":"29","main_file_link":[{"url":"https://arxiv.org/abs/1902.07330","open_access":"1"}],"isi":1,"abstract":[{"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.","lang":"eng"}],"oa":1,"year":"2023"}