High-order persistence of resonant caustics in perturbed circular billiards
We find necessary and sufficient conditions for high-order persistence of resonant caustics in perturbed circular billiards. The main tool is a perturbation theory based on the Bialy–Mironov generating function for convex billiards. All resonant caustics with period q persist up to order ceil(q/n)-1...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/450169 |
| Acceso en línea: | https://hdl.handle.net/2117/450169 https://dx.doi.org/10.1017/etds.2025.10248 |
| Access Level: | acceso abierto |
| Palabra clave: | Convex billiards Twist maps Periodic orbits Invariant curves Perturbation theory |
| Sumario: | We find necessary and sufficient conditions for high-order persistence of resonant caustics in perturbed circular billiards. The main tool is a perturbation theory based on the Bialy–Mironov generating function for convex billiards. All resonant caustics with period q persist up to order ceil(q/n)-1 under any polynomial deformation of the circle of degree n. |
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