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 §5 we prove some estimates for the topological entropy of Lorentz gas.
Original language | English (US) |
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Pages (from-to) | 791-805 |
Number of pages | 15 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 18 |
Issue number | 4 |
DOIs | |
State | Published - Aug 1998 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics