Communications in Mathematical Physics

, Volume 217, Issue 1, pp 33–53 | Cite as

Hyperbolic Magnetic Billiards on Surfaces¶of Constant Curvature

  • Boris Gutkin

Abstract:

We consider classical billiards on surfaces of constant curvature, where the charged billiard ball is exposed to a homogeneous, stationary magnetic field perpendicular to the surface.

We establish sufficient conditions for hyperbolicity of the billiard dynamics, and give a lower estimation for the Lyapunov exponent. This extends our recent results for non-magnetic billiards on surfaces of constant curvature. Using these conditions, we construct large classes of magnetic billiard tables with positive Lyapunov exponents on the plane, on the sphere and on the hyperbolic plane.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Boris Gutkin
    • 1
  1. 1.Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel.¶E-mail: fegutkin@vegas.weizmann.ac.ilIL

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