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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.01362 |
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| _version_ | 1866929249294745600 |
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| author | Bessa, Mário Del Magno, Gianluigi Dias, João Lopes Gaivão, José Pedro Torres, Maria Joana |
| author_facet | Bessa, Mário Del Magno, Gianluigi Dias, João Lopes Gaivão, José Pedro Torres, Maria Joana |
| contents | We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01362 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Billiards in generic convex bodies have positive topological entropy Bessa, Mário Del Magno, Gianluigi Dias, João Lopes Gaivão, José Pedro Torres, Maria Joana Dynamical Systems We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits. |
| title | Billiards in generic convex bodies have positive topological entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2201.01362 |