Hyperbolic Billiards on Surfaces of Constant Curvature

B. Gutkin; U. Smilansky; E. Gutkin

doi:10.1007/s002200050748

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arXiv · chao-dyn/9905030

Hyperbolic Billiards on Surfaces of Constant Curvature

B. Gutkin·U. Smilansky·E. Gutkin

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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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B. Gutkin, U. Smilansky, E. Gutkin. 1999-05-18. Hyperbolic Billiards on Surfaces of Constant Curvature. https://doi.org/10.1007/s002200050748

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