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2 results

  • Topological entropy of semi-dispersing billiards

  • D. BURAGO, S. FERLEGER, A. KONONENKO
  • Journal:
    Ergodic Theory and Dynamical Systems / Volume 18 / Issue 4 / August 1998
    Published online by Cambridge University Press:
    01 August 1998, pp. 791-805
    Print publication:
    August 1998

  • 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.