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Gibbs Measures in Ergodic Theory
Russian Mathematical Surveys, 1972In 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 ...
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1983
The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently ...
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The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently ...
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On the Ergodic Theory of Markov Chains
Operations Research, 1973This paper presents results in the ergodic theory of Markov chains that are useful in certain cases where the well known theory of Foster and Pakes is not applicable. The paper gives the background leading to the results, describes their significance, proves two theorems, and presents an example.
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