Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T00:50:38.001Z Has data issue: false hasContentIssue false
  • English
  • Français

The complete hyperbolicity of cylindric billiards

Published online by Cambridge University Press:  09 January 2002

NÁNDOR SIMÁNYI
NÁNDOR SIMÁNYI
Affiliation:
University of Alabama at Birmingham, Department of Mathematics, Campbell Hall, Birmingham, AL 35294, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 1 , February 2002 , pp. 281 - 302
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)