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A geometric approach to semi-dispersing billiards (Survey)

Published online by Cambridge University Press:  01 April 1998

D. BURAGO ,
S. FERLEGER  and
A. KONONENKO
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)
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Abstract

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We summarize the results of several recent papers, together with a few new results, which rely on a connection between semi-dispersing billiards and non-regular Riemannian geometry. We use this connection to solve several open problems about the existence of uniform estimates on the number of collisions, topological entropy and periodic trajectories of such billiards.

Type
Review Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 2 , April 1998 , pp. 303 - 319
Copyright
1998 Cambridge University Press