Caustic-Free Regions for Billiards on Surfaces of Constant Curvature

Autor:	Florentin, Dan Itzhak, Ostrover, Yaron, Rosen, Daniel
Rok vydání:	2021
Předmět:	Mathematics - Dynamical Systems Mathematics - Metric Geometry 52A10 52A55 37E40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 17 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.04914 Zobrazit plný text záznamu View this record from Arxiv