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Uspekhi Mat. Nauk, 1972, Volume 27, Issue 4(166), Pages 21–64 (Mi umn5083)  

This article is cited in 303 scientific papers (total in 305 papers)

Gibbs measures in ergodic theory

Ya. G. Sinai

Abstract: In this paper we introduce the concept of a Gibbs measure, which generalizes the concept of an equilibrium Gibbs distribution in statistical physics. The new concept is important in the study of Anosov dynamical systems. By means of this concept we construct a wide class of invariant measures for dynamical systems of this kind and investigate the problem of the existence of an invariant measure consistent with a smooth structure on the manifold; we also study the behaviour under small random excitations as $\epsilon\to 0$. The cases of discrete time and continuous time are treated separately.

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English version:
Russian Mathematical Surveys, 1972, 27:4, 21–69

Bibliographic databases:

UDC: 519.5+519.24
MSC: 37A35, 37A30, 37D20

Citation: Ya. G. Sinai, “Gibbs measures in ergodic theory”, Uspekhi Mat. Nauk, 27:4(166) (1972), 21–64; Russian Math. Surveys, 27:4 (1972), 21–69

Citation in format AMSBIB
\by Ya.~G.~Sinai
\paper Gibbs measures in ergodic theory
\jour Uspekhi Mat. Nauk
\yr 1972
\vol 27
\issue 4(166)
\pages 21--64
\jour Russian Math. Surveys
\yr 1972
\vol 27
\issue 4
\pages 21--69

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