Area spectral rigidity for axially symmetric symplectic billiard tables
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918488697733120 |
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| author | Baracco, Luca Bernardi, Olga Nardi, Alessandra |
| author_facet | Baracco, Luca Bernardi, Olga Nardi, Alessandra |
| contents | We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this class is necessarily equi-affine. We use techniques, adapted to symplectic billiards, inspired to the paper by J. De Simoi, V. Kaloshin and Q. Wei (2017). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Area spectral rigidity for axially symmetric symplectic billiard tables Baracco, Luca Bernardi, Olga Nardi, Alessandra Dynamical Systems 37C83, 58J53 We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this class is necessarily equi-affine. We use techniques, adapted to symplectic billiards, inspired to the paper by J. De Simoi, V. Kaloshin and Q. Wei (2017). |
| title | Area spectral rigidity for axially symmetric symplectic billiard tables |
| topic | Dynamical Systems 37C83, 58J53 |
| url | https://arxiv.org/abs/2410.12644 |