Symmetric periodic orbits in symmetric billiards

Abstract

Abstract In this text we study billiards on symmetric ovals and investigate some consequences of the symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits with the same symmetry of the boundary which always exist and prove that typically half of them are elliptic and Moser stable and the other half are hyperbolic with homo(hetero)clinic intersections.