Caustic-Free Regions for Billiards in the Hyperbolic Plane

Dan Itzhak Florentin, Yaron Ostrover, Daniel Rosen

Published 2021-02-09Version 1

In this note we study caustic-free regions for convex billiard tables in the hyperbolic plane. 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 the setting of the hyperbolic plane a theorem due to Hubacher which shows that no caustics exist near the boundary of a convex billiard table whose curvature is discontinuous.