High-order persistence of resonant caustics in perturbed circular billiards
Dynamical Systems
2026-01-14 v2
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 persist up to order under any polynomial deformation of the circle of degree .
Keywords
Cite
@article{arxiv.2503.07488,
title = {High-order persistence of resonant caustics in perturbed circular billiards},
author = {Comlan Edmond Koudjinan and Rafael Ramírez-Ros},
journal= {arXiv preprint arXiv:2503.07488},
year = {2026}
}
Comments
26 pages, 1 color figure