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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.18433 |
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| _version_ | 1866915355192983552 |
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| author | Li, Zaicun |
| author_facet | Li, Zaicun |
| contents | We study outer billiard systems around a class of circular sectors. For semi-discs, we prove the existence of elliptic islands occupying a positive proportion of the plane. Combined with known results, this shows the coexistence of stability and diffusion for this system.
On the other hand, we show that there exists a countable family of circular sectors for which the outer billiard system has zero measure of escaping orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic islands and zero measure escaping orbits in a class of outer billiards Li, Zaicun Dynamical Systems We study outer billiard systems around a class of circular sectors. For semi-discs, we prove the existence of elliptic islands occupying a positive proportion of the plane. Combined with known results, this shows the coexistence of stability and diffusion for this system. On the other hand, we show that there exists a countable family of circular sectors for which the outer billiard system has zero measure of escaping orbits. |
| title | Elliptic islands and zero measure escaping orbits in a class of outer billiards |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2506.18433 |