The Complete Hyperbolicity of Cylindric Billiards

Details The Complete Hyperbolicity of Cylindric Billiards The Complete Hyperbolicity of Cylindric Billiards

1999-06-21

arxiv.org/abs/math/9906139v1

Ergodic theory and dynamical systems, Vol. 22 (2002), 281-302

Mathematics

Dynamical Systems

22 pages

Scientific paper

10.1017/S0143385702000135

The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with specular reflections at the boundaries of the removed cylinders. It is proven here that under a certain geometric condition --- slightly stronger than the necessary condition presented in [S-Sz(1998)] --- a cylindric billiard flow is completely hyperbolic. As a consequence, every hard ball system is completely hyperbolic --- a result strengthening the theorem of [S-Sz(1999)].

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