Birkhoff attractors of dissipative billiards
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929751926505472 |
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| author | Bernardi, Olga Florio, Anna Leguil, Martin |
| author_facet | Bernardi, Olga Florio, Anna Leguil, Martin |
| contents | We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of the attractor, in terms both of the geometry of the billiard table and of the strength of the dissipation. We focus on the study of an invariant subset of the attractor, the so-called Birkhoff attractor. On the one hand, we show that for a generic convex table with "pinched" curvature, the Birkhoff attractor is a normally contracted manifold when the dissipation is strong. On the other hand, for a mild dissipation, we prove that generically the Birkhoff attractor is complicated, both from the topological and the dynamical point of view. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07342 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Birkhoff attractors of dissipative billiards Bernardi, Olga Florio, Anna Leguil, Martin Dynamical Systems 37C83, 37B35, 37C70, 37D45, 37G35 We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of the attractor, in terms both of the geometry of the billiard table and of the strength of the dissipation. We focus on the study of an invariant subset of the attractor, the so-called Birkhoff attractor. On the one hand, we show that for a generic convex table with "pinched" curvature, the Birkhoff attractor is a normally contracted manifold when the dissipation is strong. On the other hand, for a mild dissipation, we prove that generically the Birkhoff attractor is complicated, both from the topological and the dynamical point of view. |
| title | Birkhoff attractors of dissipative billiards |
| topic | Dynamical Systems 37C83, 37B35, 37C70, 37D45, 37G35 |
| url | https://arxiv.org/abs/2311.07342 |