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 q/n -1 under any polynomial deformation of the circle of degree n.
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