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Ergodic Theory

  • Ya. G. Sinai
Part of the Acta Physica Austriaca book series (FEWBODY, volume 10/1973)

Abstract

Apparently there are at least two reasons why ergodic theory has the honour to be discussed at this solemn Conference. The first reason follows from the fact that Ludwig Boltzmann is one of the founders of ergodic theory. The term “ergodicity” was introduced by Ludwig Boltzmann in his paper [1] in 1887 (see also his “Lectures on Gas Theory”). In fact it is connected with another remarkable discovery by Boltzmann of how dynamical laws of motions can lead to statistics. As a result, ergodic theory is a branch of mathematics which investigates statistical properties of dynamical systems. The second reason is that the concepts of ergodicity and mixing of Ludwig Boltzmann and J. Gibbs have become very fruitful and given many new notions, ideas and results of a general character. The mathematics clarified the essence of these concepts and gave deeper penetration into many problems. This led to some progress in the solution of these problems.

Keywords

Phase Space Ergodic Theory Topological Entropy Invariant Torus Invariant Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Ya. G. Sinai
    • 1
  1. 1.Landau Institute for Theoretical PhysicsAcademy of SciencesUSSR

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