Ergodicity of asymmetric lemon Billiards
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909909339078656 |
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| author | Fan, Wentao Hasselblatt, Boris |
| author_facet | Fan, Wentao Hasselblatt, Boris |
| contents | We show ergodicity of (asymmetric) lemon billiards, billiard tables that are the intersection of two circles of which one contains the centers of both. These do not satisfy the Wojtkowski criteria for hyperbolicity, but we establish \emph{uniform} expansion of vectors in an invariant cone family and alignment of singularity curves. Both of these are difficult, and the approach to the latter seems new. Together, these properties imply ergodicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity of asymmetric lemon Billiards Fan, Wentao Hasselblatt, Boris Dynamical Systems We show ergodicity of (asymmetric) lemon billiards, billiard tables that are the intersection of two circles of which one contains the centers of both. These do not satisfy the Wojtkowski criteria for hyperbolicity, but we establish \emph{uniform} expansion of vectors in an invariant cone family and alignment of singularity curves. Both of these are difficult, and the approach to the latter seems new. Together, these properties imply ergodicity. |
| title | Ergodicity of asymmetric lemon Billiards |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.04948 |