1. Topological entropy of semi-dispersing billiards
- Author
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S. Ferleger, Dmitri Burago, and A. Kononenko
- Subjects
Applied Mathematics ,General Mathematics ,Lorentz transformation ,Mathematical analysis ,Boundary (topology) ,Topological entropy ,Riemannian geometry ,Manifold ,Nonlinear Sciences::Chaotic Dynamics ,symbols.namesake ,Flow (mathematics) ,symbols ,Sectional curvature ,Dynamical billiards ,Mathematics - Abstract
In this paper we continue to explore the applications of the connections between singular Riemannian geometry and billiard systems that were first used in [6] to prove estimates on the number of collisions in non-degenerate semi-dispersing billiards.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 of a simple-connected billiard table) and the number of periodic trajectories (for the billiard flow). In \S5 we prove some estimates for the topological entropy of Lorentz gas.
- Published
- 1998