High-order persistence of resonant caustics in perturbed circular billiards
Comlan Edmond Koudjinan, Rafael Ramírez-Ros
公開日: 2025/3/10
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 $n$.