- 01-245 P. B\'alint, N. Chernov, P. T\'oth, D. Sz\'asz
- Geometry of Multi-dimensional Dispersing Billiards
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.