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Topological entropy of semi-dispersing billiards

Published online by Cambridge University Press:  01 August 1998


D. BURAGO
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: \{burago, ferleger\}@math.psu.edu)
S. FERLEGER
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: \{burago, ferleger\}@math.psu.edu)
A. KONONENKO
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA (e-mail: alexko@math.upenn.edu)

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.


Type
Research Article
Copyright
© 1998 Cambridge University Press

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