High-order persistence of resonant caustics in perturbed circular billiards
Abstract 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 $\lceil q/n \rceil -1$ under any polynomial deformation of the circle of degree n .
Authors
- Comlan Edmond Koudjinan (ORCID: https://orcid.org/0000-0003-2640-4049)
- Rafael Ramírez-Ros (ORCID: https://orcid.org/0000-0002-2127-2940)
Institutions
- University of Toronto (CA)
- Universitat Politècnica de Catalunya (ES)
Publication Details
- Journal
- Ergodic Theory and Dynamical Systems
- Published
- 2025-10-23
- DOI
- https://doi.org/10.1017/etds.2025.10248
- Primary Topic
- Quantum chaos and dynamical systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00