TY - JOUR
T1 - Caustic-free regions for billiards on surfaces of constant curvature
AU - Florentin, Dan Itzhak
AU - Ostrover, Yaron
AU - Rosen, Daniel
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/10
Y1 - 2021/10
N2 - 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.
AB - 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.
KW - Billiards
KW - Caustics
KW - Surfaces of constant curvature
UR - http://www.scopus.com/inward/record.url?scp=85107915314&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2021.104305
DO - 10.1016/j.geomphys.2021.104305
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AN - SCOPUS:85107915314
SN - 0393-0440
VL - 168
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
M1 - 104305
ER -