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<p>Given an&#xa0;ergodic flow, we realize the range of convergence rates of Birkhoff averages from the maximal rate to an&#xa0;arbitrarily slow rate by choosing the function to be averaged.For&#xa0;almost all torus windings, the functions to be averaged can be chosen continuous.This complements the classical result of Krengel on slow convergence rates of averages for ergodic automorphisms.</p>

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The Full Range of Convergence Rates of Birkhoff Averages for Ergodic Flows

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • I. V. Podvigin,
  • V. V. Ryzhikov

摘要

Given an ergodic flow, we realize the range of convergence rates of Birkhoff averages from the maximal rate to an arbitrarily slow rate by choosing the function to be averaged.For almost all torus windings, the functions to be averaged can be chosen continuous.This complements the classical result of Krengel on slow convergence rates of averages for ergodic automorphisms.