Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps

Abstract

For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the necessary condition for the corresponding billiard map to keep the coexistence of periodic $2,3$ caustics is that the deformation has to be an isometric transformation.

Cited by in corpus (1)

• High-order persistence of resonant caustics in perturbed circular billiards