97-151 D.Burago, F.Ferleger, A.Kononenko

Topological entropy of semi-dispersing billiards. (56K, Latex 2e) Apr 1, 97

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Abstract. In this paper we continue to explore the applications of the connections between singular Riemannian geometry and billiard systems that were used to prove local estimates on the number of collisions in non-degenerate semi-dispersing billiards in our previous paper. In this paper we show that the topological entropy of a compact non-degenerate semi-dispersing billiard on any manifold of non-positive sectional curvature is finite. Also, we prove exponential estimates on the number of periodic points (for the first return map to the boundary) and the number of periodic trajectories (for the billiard flow). In the last Section we prove some estimates for the topological entropy of Lorentz gas.

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