A geometric approach to semi-dispersing billiards

Dmitri Burago; S. Ferleger; A. Kononenko

doi:10.1017/S014338579811564X

A geometric approach to semi-dispersing billiards

Dmitri Burago, S. Ferleger, A. Kononenko

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	303-319
Number of pages	17
Journal	Ergodic Theory and Dynamical Systems
Volume	18
Issue number	2
DOIs	https://doi.org/10.1017/S014338579811564X
State	Published - Jan 1 1998

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "A geometric approach to semi-dispersing billiards",

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.",

author = "Dmitri Burago and S. Ferleger and A. Kononenko",

year = "1998",

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AU - Ferleger, S.

AU - Kononenko, A.

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N2 - 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.

AB - 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.

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A geometric approach to semi-dispersing billiards

Abstract

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