Length spectrum rigidity for piecewise analytic Bunimovich billiards
Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 1–50.
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Author
Chen, Jianyu;
Kaloshin, VadimISTA 
;
Zhang, Hong Kun
;
Zhang, Hong KunCorresponding author has ISTA affiliation
Department
Abstract
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.
Publishing Year
Date Published
2023-11-01
Journal Title
Communications in Mathematical Physics
Publisher
Springer Nature
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).
Volume
404
Page
1-50
ISSN
eISSN
IST-REx-ID
Cite this
Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 2023;404:1-50. doi:10.1007/s00220-023-04837-z
Chen, J., Kaloshin, V., & Zhang, H. K. (2023). Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04837-z
Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04837-z.
J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” Communications in Mathematical Physics, vol. 404. Springer Nature, pp. 1–50, 2023.
Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 1–50.
Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” Communications in Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 1–50, doi:10.1007/s00220-023-04837-z.
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