99-76 P\'eter B\'alint

Chaotic and Ergodic Properties of Cylindric Billiards (98K, LaTeX 2e) Mar 16, 99

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Abstract. Chaotic and ergodic properties are discussed in this paper for various subclasses of cylindric billiards. Common feature of the studied systems is that they satisfy a natural necessary condition for ergodicity and hyperbolicity, the so called transitivity condition. 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 ohter 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.

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