The complete hyperbolicity of cylindric billiards

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 a cylindric billiard flow is completely hyperbolic. As a consequence, every hard ball system is completely hyperbolic.

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