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A geometric approach to semi-dispersing billiards (Survey)

Published online by Cambridge University Press:  01 April 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

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
Copyright
1998 Cambridge University Press

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