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On the convergence of bilateral ergodic averages

Volume 164 / 2021

Christophe Cuny, Yves Derriennic Colloquium Mathematicum 164 (2021), 327-339 MSC: Primary 37A05. DOI: 10.4064/cm7985-3-2020 Published online: 13 November 2020

Abstract

We study the almost sure convergence of bilateral ergodic averages for not necessarily integrable functions and relate it to the convergence of forward and backward averages, hence complementing results of Woś and the second named author. In the case of convergence, using results of Furstenberg on double recurrence, we prove oscillations of the bilateral ergodic averages around the limit.

Authors

  • Christophe CunyUniversité de Brest
    Mathématiques (LMBA-UMR CNRS 6205)
    6 av. Le Gorgeu
    29238 Brest, France
    e-mail
  • Yves DerriennicUniversité de Brest
    Mathématiques (LMBA-UMR CNRS 6205)
    6 av. Le Gorgeu
    29238 Brest, France
    e-mail

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