Integrable Billiards and Related Topics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866918163083427840 |
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| author | Bialy, Misha Mironov, Andrey E. |
| author_facet | Bialy, Misha Mironov, Andrey E. |
| contents | This paper surveys our results on integrable billiards. We consider various models of billiards, including Birkhoff, outer, magnetic, and Minkowski billiards. Also, we discuss wire billiards and billiards in cones. For four models of convex plane billiards, we also discuss an isoperimetric-type inequality for the Mather $β$-function. We conclude with a section of open questions on this subject. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrable Billiards and Related Topics Bialy, Misha Mironov, Andrey E. Dynamical Systems Differential Geometry This paper surveys our results on integrable billiards. We consider various models of billiards, including Birkhoff, outer, magnetic, and Minkowski billiards. Also, we discuss wire billiards and billiards in cones. For four models of convex plane billiards, we also discuss an isoperimetric-type inequality for the Mather $β$-function. We conclude with a section of open questions on this subject. |
| title | Integrable Billiards and Related Topics |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2510.03790 |