Weak mixing in rational billiards
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912073228746752 |
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| author | Arana-Herrera, Francisco Chaika, Jon Forni, Giovanni |
| author_facet | Arana-Herrera, Francisco Chaika, Jon Forni, Giovanni |
| contents | We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak mixing in rational billiards Arana-Herrera, Francisco Chaika, Jon Forni, Giovanni Dynamical Systems 37A25, 37C83, 37E35. 37F34 We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle. |
| title | Weak mixing in rational billiards |
| topic | Dynamical Systems 37A25, 37C83, 37E35. 37F34 |
| url | https://arxiv.org/abs/2410.11117 |