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

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2026, Volume: 67, Number: 4, Pages: 846-855 Pages count : 10 DOI: 10.1134/s0037446626040105
Tags convergence rates in ergodic theorems, special representation of a flow, odometer, torus winding
Authors Podvigin I.V. 1 , Ryzhikov V.V. 2
Affiliations
1 Sobolev Institute of Mathematics, Novosibirsk, Russia
2 Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Funding (1)

1 Министерство науки и высшего образования РФ FWNF-2026-0022

Abstract: 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.
Cite: Podvigin I.V. , Ryzhikov V.V.
The Full Range of Convergence Rates of Birkhoff Averages for Ergodic Flows
Siberian Mathematical Journal. 2026. V.67. N4. P.846-855. DOI: 10.1134/s0037446626040105 OpenAlex
Original: Подвигин И.В. , Рыжиков В.В.
Полный диапазон скоростей сходимости средних Биркгофа для эргодических потоков
Сибирский математический журнал. 2026. Т.67. №4. С.690-702. DOI: 10.33048/smzh.2026.67.410
Dates:
Submitted: Jan 24, 2024
Accepted: Feb 25, 2025
Published online: Jul 30, 2026
Identifiers:
≡ OpenAlex: W7171854599
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