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Uspekhi Mat. Nauk, 1970, Volume 25, Issue 2(152), Pages 141–192 (Mi umn5322)  

This article is cited in 512 scientific papers (total in 516 papers)

Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards

Ya. G. Sinai

Abstract: In this paper we consider dynamical systems resulting from the motion of a material point in domains with strictly convex boundary, that is, such that the operator of the second quadratic form is negative-definite at each point of the boundary, where the boundary is taken to be equipped with the field of inward normals. We prove that such systems are ergodic and are $K$-systems. The basic method of investigation is the construction of transversal foliations for such systems and the study of their properties.

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English version:
Russian Mathematical Surveys, 1970, 25:2, 137–189

Bibliographic databases:

UDC: 518.25
MSC: 37N05, 37Axx, 37D50, 37D40
Received: 11.12.1969

Citation: Ya. G. Sinai, “Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards”, Uspekhi Mat. Nauk, 25:2(152) (1970), 141–192; Russian Math. Surveys, 25:2 (1970), 137–189

Citation in format AMSBIB
\by Ya.~G.~Sinai
\paper Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards
\jour Uspekhi Mat. Nauk
\yr 1970
\vol 25
\issue 2(152)
\pages 141--192
\jour Russian Math. Surveys
\yr 1970
\vol 25
\issue 2
\pages 137--189

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