Hyperbolic Billiards on Surfaces of Constant Curvature

Details Hyperbolic Billiards on Surfaces of Constant Curvature Hyperbolic Billiards on Surfaces of Constant Curvature

1999-05-18

arxiv.org/abs/chao-dyn/9905030v1

Nonlinear Sciences

Chaotic Dynamics

28 pages, 14 postscript figures

Scientific paper

10.1007/s002200050748

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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