In this note we study caustic-free regions for convex billiard tables in the hyperbolic plane or the hemisphere. In particular, following a result by Gutkin and Katok in the Euclidean case, we estimate the size of such regions in terms of the geometry of the billiard table. Moreover, we extend to this setting a theorem due to Hubacher which shows that no caustics exist near the boundary of a convex billiard table whose curvature is discontinuous.
- Surfaces of constant curvature
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology