Periodic orbits of oval billiards on surfaces of constant curvature
Periodic orbits of oval billiards on surfaces of constant curvature
In this paper, we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a two-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism, if the boundary of the region is an oval. Using these properties and defining …