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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.17985 |
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| _version_ | 1866910663468646400 |
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| author | Gogolev, Andrey Keck, Levi Lewis, Kevin |
| author_facet | Gogolev, Andrey Keck, Levi Lewis, Kevin |
| contents | We introduce a new class of billiard-like system, ``bouncing outer billiards" which are 3-dimensional cousins of outer billiards of Neumann and Moser. We prove that bouncing outer billiard on a smooth convex body has at least four 1-parameter families of fixed points. We also fully describe dynamics of bouncing outer billiard on a line segment. Finally we carry out numerical experiments suggesting very complicated (non-ergodic) behavior for several shapes including the square and an ellipse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17985 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bouncing Outer Billiards Gogolev, Andrey Keck, Levi Lewis, Kevin Dynamical Systems We introduce a new class of billiard-like system, ``bouncing outer billiards" which are 3-dimensional cousins of outer billiards of Neumann and Moser. We prove that bouncing outer billiard on a smooth convex body has at least four 1-parameter families of fixed points. We also fully describe dynamics of bouncing outer billiard on a line segment. Finally we carry out numerical experiments suggesting very complicated (non-ergodic) behavior for several shapes including the square and an ellipse. |
| title | Bouncing Outer Billiards |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.17985 |