Local rigidity for symplectic billiards
Tsodikovich D. 2025. Local rigidity for symplectic billiards. Journal of Geometric Analysis. 35(10), 306.
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Abstract
We show a local rigidity result for the integrability of symplectic billiards. We prove that any domain which is close to an ellipse, and for which the symplectic billiard map is rationally integrable must be an ellipse as well. This is in spirit of the result of [2] for Birkhoff billiards.
Publishing Year
Date Published
2025-08-07
Journal Title
Journal of Geometric Analysis
Publisher
Springer Nature
Acknowledgement
The author would like to thank Corentin Fierobe, Vadim Kaloshin, Illya Koval and Yunzhe Li for useful discussions. The author would also like to thank the referee for useful remarks. Open access funding provided by Institute of Science and Technology (IST Austria). European Research Council (885707) Mr Daniel Tsodikovich
Volume
35
Issue
10
Article Number
306
ISSN
IST-REx-ID
Cite this
Tsodikovich D. Local rigidity for symplectic billiards. Journal of Geometric Analysis. 2025;35(10). doi:10.1007/s12220-025-02148-4
Tsodikovich, D. (2025). Local rigidity for symplectic billiards. Journal of Geometric Analysis. Springer Nature. https://doi.org/10.1007/s12220-025-02148-4
Tsodikovich, Daniel. “Local Rigidity for Symplectic Billiards.” Journal of Geometric Analysis. Springer Nature, 2025. https://doi.org/10.1007/s12220-025-02148-4.
D. Tsodikovich, “Local rigidity for symplectic billiards,” Journal of Geometric Analysis, vol. 35, no. 10. Springer Nature, 2025.
Tsodikovich D. 2025. Local rigidity for symplectic billiards. Journal of Geometric Analysis. 35(10), 306.
Tsodikovich, Daniel. “Local Rigidity for Symplectic Billiards.” Journal of Geometric Analysis, vol. 35, no. 10, 306, Springer Nature, 2025, doi:10.1007/s12220-025-02148-4.
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