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arXiv · 2503.07488

High-order persistence of resonant caustics in perturbed circular billiards

Comlan Edmond Koudjinan·Rafael Ramírez-Ros
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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 $n$.

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Comlan Edmond Koudjinan, Rafael Ramírez-Ros. 2025-03-10. High-order persistence of resonant caustics in perturbed circular billiards. https://doi.org/10.1017/etds.2025.10248

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