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Dynamical Systems with Invariant Measure

  • A. M. Vershik
  • S. A. Yuzvinskii
Part of the Progress in Mathematics book series (PM, volume 8)

Abstract

The theory of transformations with invariant measure or the metric theory of dynamical systems or ergodic theory is extensively related to various branches of mathematics — to the theory of classical dynamical systems, i.e., to classical mechanics, to probability theory, to functional analysis, to algebra, to number theory, to topology, etc. These diverse and steadfast relationships are rooted in the following two factors: first, the basic object of study, namely, a transformation with invariant measure (in other words, an automorphism of a space with measure), frequently encountered in mathematics, has proved to be a topic which is very meaningful and which lends itself to profound study; second, ergodic theory itself has repeatedly turned out to be an area in which there have been applied and verified new powerful general mathematical ideas and methods such as operator theory, general measure theory, and quite recently, information theory and probability theory, etc.

Keywords

Invariant Measure Ergodic Theory Ergodic Theorem Lebesgue Space Geodesic Flow 
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

© Plenum Press, New York 1970

Authors and Affiliations

  • A. M. Vershik
  • S. A. Yuzvinskii

There are no affiliations available

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