High-order persistence of resonant caustics in perturbed circular billiards

2025/03/10 by Koudjinan, Comlan Edmond, Ramírez-Ros, Rafael
#37C83 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.07488

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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