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Chaotic and ergodic properties of cylindric billiards

Published online by Cambridge University Press:  01 October 1999

PÉTER BÁLINT
PÉTER BÁLINT
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1364, Budapest, P.O.B. 127, Hungary (e-mail: [email protected])
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Abstract

Chaotic and ergodic properties are discussed for various subclasses of cylindric billiards. A common feature of the studied systems is that they satisfy a natural necessary condition for ergodicity and hyperbolicity, the so-called transitivity condition. The relation of our discussion to former results on hard ball systems is twofold. On the one hand, by slight adaptation of the proofs we may discuss hyperbolic and ergodic properties of 3 or 4 particles with (possibly restricted) hard ball interactions in any dimensions. On the other hand, a key tool in our investigations is a kind of connected path formula for cylindric billiards, which together with the conservation of momenta gives back, when applied to the special case of hard ball systems, the classical connected path formula.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 5 , October 1999 , pp. 1127 - 1156
Copyright
1999 Cambridge University Press

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