Magic Billiards: the Case of Elliptical Boundaries
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912183841980416 |
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| author | Dragović, Vladimir Radnović, Milena |
| author_facet | Dragović, Vladimir Radnović, Milena |
| contents | In this work, we introduce a novel concept of magic billiards, which can be seen as an umbrella, unifying several well-known generalisations of mathematical billiards. We analyse properties of magic billiards in the case of elliptical boundaries. We provide explicit conditions for periodicity in algebro-geometric, analytic, and polynomial forms. A topological description of those billiards is given using Fomenko graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Magic Billiards: the Case of Elliptical Boundaries Dragović, Vladimir Radnović, Milena Dynamical Systems Exactly Solvable and Integrable Systems 37C83, 37J35, 37J39 In this work, we introduce a novel concept of magic billiards, which can be seen as an umbrella, unifying several well-known generalisations of mathematical billiards. We analyse properties of magic billiards in the case of elliptical boundaries. We provide explicit conditions for periodicity in algebro-geometric, analytic, and polynomial forms. A topological description of those billiards is given using Fomenko graphs. |
| title | Magic Billiards: the Case of Elliptical Boundaries |
| topic | Dynamical Systems Exactly Solvable and Integrable Systems 37C83, 37J35, 37J39 |
| url | https://arxiv.org/abs/2409.03158 |