The Complete Hyperbolicity of Cylindric Billiards
Dynamical Systems
2010-08-12 v1 Mathematical Physics
math.MP
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)].
Cite
@article{arxiv.math/9906139,
title = {The Complete Hyperbolicity of Cylindric Billiards},
author = {Nandor Simanyi},
journal= {arXiv preprint arXiv:math/9906139},
year = {2010}
}
Comments
22 pages