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DOI: https://doi.org/10.1070/RM1972v027n04ABEH001383

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.

Russian version:
Uspekhi Matematicheskikh Nauk, 1972, Volume 27, Issue 4(166), Pages 21–64

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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

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