Nandor Simanyi
The Complete Hyperbolicity of Cylindric Billiards
(70K, AMS TeX)
ABSTRACT. 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)].