We consider a simple closed and geodesically strictly convex curve on hemisphere or hyperbolic plane and a moving particle free geodesic within the region bounded by this curve suffering elastic collisions with the curve ...

Let Q be a strictly geodesically convex region in the hyperbolic plane bounded by a closed curve with strictly positive geodesic curvature. A billiard on Q consists in the particle’s free motion suffering elastic collisions ...

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 ...

In this work we extend some results about plane billiards to the hyperbolic plane and to ahemisphere of the sphere. First we consider billiards defined in the region bounded by a closed and geodesically strictly convex ...