01-245 P. B\'alint, N. Chernov, P. T\'oth, D. Sz\'asz

Geometry of Multi-dimensional Dispersing Billiards (720K, Postscript) Jul 6, 01

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Abstract. Geometric properties of multi-dimensional dispersing billiards are studied in this paper. On the one hand, non-smooth behaviour in the singularity submanifolds of the system is discovered (this discovery applies to the more general class of semi-dispersing billiards as well). On the other hand, a self-contained geometric description for unstable manifolds is given, together with the proof of important regularity properties. All these issues are highly relevant to studying the ergodic and statistical behaviour of the dynamics.

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