- 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
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
In this paper we show that the topological entropy of a compact
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.