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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
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
Citation:
L. A. Bunimovich, “Absolute Focusing and Ergodicity of Billiards”, Regul. Chaotic Dyn., 8:1 (2003), 15–28
Linking options:
https://www.mathnet.ru/eng/rcd762 https://www.mathnet.ru/eng/rcd/v8/i1/p15
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Abstract page: | 92 |
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