Marked Length Spectral determination of analytic chaotic billiards with axial symmetries
De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 233, 829–901.
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Author
De Simoi, Jacopo;
Kaloshin, VadimISTA 
;
Leguil, Martin
;
Leguil, MartinDepartment
Abstract
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.
Publishing Year
Date Published
2023-08-01
Journal Title
Inventiones Mathematicae
Publisher
Springer Nature
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.
Volume
233
Page
829-901
ISSN
eISSN
IST-REx-ID
Cite this
De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 2023;233:829-901. doi:10.1007/s00222-023-01191-8
De Simoi, J., Kaloshin, V., & Leguil, M. (2023). Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-023-01191-8
De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” Inventiones Mathematicae. Springer Nature, 2023. https://doi.org/10.1007/s00222-023-01191-8.
J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination of analytic chaotic billiards with axial symmetries,” Inventiones Mathematicae, vol. 233. Springer Nature, pp. 829–901, 2023.
De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 233, 829–901.
De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” Inventiones Mathematicae, vol. 233, Springer Nature, 2023, pp. 829–901, doi:10.1007/s00222-023-01191-8.
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