Caustic-free regions for billiards on surfaces of constant curvature

Dan Itzhak Florentin, Yaron Ostrover, Daniel Rosen

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number104305
JournalJournal of Geometry and Physics
Volume168
DOIs
StatePublished - Oct 2021

Keywords

  • Billiards
  • Caustics
  • Surfaces of constant curvature

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