Gibbs measures in ergodic theory

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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 (formula presented.) The cases of discrete time and continuous time are treated separately.

Original languageEnglish (US)
Pages (from-to)21-69
Number of pages49
JournalRussian Mathematical Surveys
Volume27
Issue number4
DOIs
StatePublished - Aug 31 1972

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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