Caustic-free regions for billiards on surfaces of constant curvature

Dan Itzhak Florentin, Yaron Ostrover, Daniel Rosen

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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
StatePublished - Oct 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.


Acknowledgments: We are grateful to Misha Bialy and Serge Tabachnikov for useful comments. DIF was partially supported by the U.S. National Science Foundation Grant DMS-1101636 . YO is partially supported by the European Research Council starting grant No. 637386 , and by the ISF grant No. 667/18 . DR is partially supported by the SFB/TRR 191 ‘Symplectic Structures in Geometry, Algebra and Dynamics’, funded by the DFG (Projektnummer 281071066 – TRR 191).

FundersFunder number
National Science FoundationDMS-1101636
European Research Council637386
Deutsche Forschungsgemeinschaft281071066 – TRR 191
Israel Science Foundation667/18, SFB/TRR 191


    • Billiards
    • Caustics
    • Surfaces of constant curvature


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