The Pointwise Ergodic Theorem

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


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.




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

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© Springer-Verlag London 2016

Authors and Affiliations

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

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