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The Pointwise Ergodic Theorem

  • Yves Coudène
Chapter
Part of the Universitext book series (UTX)

Abstract

Consider a dynamical system, modeled by the data of a phase space X, a transformation T: X → X describing the evolution of the system over time, and a finite measure μ representing an extensive quantity conserved during the motion. We wish to study the sequence {T n (x)}n ∈ N, which represents the succession of states the system takes on over time. This sequence makes up the trajectory of the point x, or its orbit.

Keywords

Conditional Expectation Ergodic Theorem Finite Measure Observable Quantity Maximal Inequality 
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.

References

  1. 13.
    Krengel, U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter & Co., Berlin (1985)Google Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Yves Coudène
    • 1
  1. 1.Université de Bretagne OccidentaleBrestFrance

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