The Full Range of Convergence Rates of Birkhoff Averages for Ergodic Flows Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| 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 | ||||
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| Affiliations |
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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
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
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 |