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Regular and Chaotic Dynamics, 2003, Volume 8, Issue 1, Pages 15–28
DOI: https://doi.org/10.1070/RD2003v008n01ABEH000223
(Mi rcd762)
 

This article is cited in 4 scientific papers (total in 4 papers)

Dynamics of billiards

Absolute Focusing and Ergodicity of Billiards

L. A. Bunimovich

Southeast Applied Analysis Center and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332–0160, USA
Citations (4)
Abstract: We show that absolute focusing is a necessary condition for a focusing component to be a part of the boundary of a hyperbolic billiard. A sketch of the proof of a general theorem on hyperbolicity and ergodicity of two-dimensional billiards with all three (focusing, dispersing and neutral) components of the boundary is given. The example of a simply connected domain (container) is given, where a system of $N$ elastically colliding balls is ergodic for any $1 \leqslant N < \infty$.
Received: 13.02.2003
Bibliographic databases:
Document Type: Article
MSC: 37E99, 37A05
Language: English
Citation: L. A. Bunimovich, “Absolute Focusing and Ergodicity of Billiards”, Regul. Chaotic Dyn., 8:1 (2003), 15–28
Citation in format AMSBIB
\Bibitem{Bun03}
\by L. A. Bunimovich
\paper Absolute Focusing and Ergodicity of Billiards
\jour Regul. Chaotic Dyn.
\yr 2003
\vol 8
\issue 1
\pages 15--28
\mathnet{http://mi.mathnet.ru/rcd762}
\crossref{https://doi.org/10.1070/RD2003v008n01ABEH000223}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1963965}
\zmath{https://zbmath.org/?q=an:1075.37517}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003RCD.....8...15B}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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