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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: simanyi@math.uab.edu)
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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

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