Conditions of stochasticity of two-dimensional billiards

Chaos
L. A. Bunimovich

Abstract

There are two known mechanisms that produce chaos in billiard systems. The first one, discovered by Ya. G. Sinai, is called dispersing, the second, found by the author, is called defocusing. The same mechanisms produce chaos for geodesic flows. Some results on two-dimensional billiards, which indicate that only these two mechanisms can produce chaos in Hamiltonian systems, are discussed.

Citations

Jul 5, 2011·Chaos·A CaratiL Galgani
Jul 5, 2012·Chaos·Alexei B Ryabov, Alexander Loskutov
Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Papenbrock
Apr 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G A Luna-AcostaA Krokhin
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Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B DietzT H Seligmann
Jan 1, 2021·Chaos·Gregory PageJulian Talbot
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B DietzF Schäfer

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