Bilhares em ovais com simetria de rotação

Abstract

We study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain some results. We prove that symmetric oval billiards have stable periodic orbits.Suficiently differentiable oval billiards always have invariant rotational curves, but there are only two types of ovals with an invariant horizontal circle in its phase-space: the constant width ovals and some very special symmetric curves. we study the dynamics near the horizontal circles of the billiard map on these ovals, and show that these horizontal circlesare approached, from both sides, by other invariant rotational curves.