Local rigidity for symplectic billiards
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915469279100928 |
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| author | Tsodikovich, Daniel |
| author_facet | Tsodikovich, Daniel |
| contents | 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 Avila, De Simoi, and Kaloshin for Birkhoff billiards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local rigidity for symplectic billiards Tsodikovich, Daniel Dynamical Systems 37C05 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 Avila, De Simoi, and Kaloshin for Birkhoff billiards. |
| title | Local rigidity for symplectic billiards |
| topic | Dynamical Systems 37C05 |
| url | https://arxiv.org/abs/2501.08849 |