Curvas invariantes de bilhares convexos em superfícies.

Abstract

This work presents a framework for billiards on convex domains in a two dimensional Riemannian manifold. In this context, some basic properties that have long been known for billiards on the plane such as differentiability and twist property are established. We deduce a formula for the billiard derivative and investigate conditions for the existence and non existence of rotational invariant curve, extending Hubacher, Mather and Douady-Lazutikin's results. We also prove there are geodesic circles such that the billiard map is not totally integrable.