Elliptic islands and zero measure escaping orbit in a class of outer billiards
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| Názov: | Elliptic islands and zero measure escaping orbit in a class of outer billiards |
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| Autori: | Li, Zaicun |
| Zdroj: | Discrete and Continuous Dynamical Systems. 47:144-189 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | American Institute of Mathematical Sciences (AIMS), 2026. |
| Rok vydania: | 2026 |
| Predmety: | FOS: Mathematics, Dynamical Systems (math.DS), Dynamical Systems |
| Popis: | 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. |
| Druh dokumentu: | Article |
| ISSN: | 1553-5231 1078-0947 |
| DOI: | 10.3934/dcds.2025115 |
| DOI: | 10.48550/arxiv.2506.18433 |
| Prístupová URL adresa: | http://arxiv.org/abs/2506.18433 |
| Rights: | CC BY |
| Prístupové číslo: | edsair.doi.dedup.....e9704853c491001e499b8f59d7efb4c1 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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. |
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| ISSN: | 15535231 10780947 |
| DOI: | 10.3934/dcds.2025115 |