Communications in Mathematical Physics

, Volume 208, Issue 1, pp 65–90 | Cite as

Hyperbolic Billiards on Surfaces of Constant Curvature

  • Boris Gutkin
  • Uzy Smilansky
  • Eugene Gutkin
Original article

Abstract:

We establish sufficient conditions for the hyperbolicity of the billiard dynamics on surfaces of constant curvature. This extends known results for planar billiards. Using these conditions, we construct large classes of billiard tables with positive Lyapunov exponents on the sphere and on the hyperbolic plane.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Boris Gutkin
    • 1
  • Uzy Smilansky
    • 1
  • Eugene Gutkin
    • 2
  1. 1.Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel.¶E-mail: fegutkin@vegas.weizmann.ac.ilIL
  2. 2.Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, USA.¶E-mail: egutkin@math.usc.eduUS

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