Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Russian Mathematical Surveys, 1996, Volume 51, Issue 4, Pages 653–703
DOI: https://doi.org/10.1070/RM1996v051n04ABEH002964
(Mi rm995)
 

This article is cited in 117 scientific papers (total in 117 papers)

The rate of convergence in ergodic theorems

A. G. Kachurovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Received: 15.01.1996
Bibliographic databases:
Document Type: Article
UDC: 517.987+519.214
MSC: 41A25, 37A30, 37A25
Language: English
Original paper language: Russian
Citation: A. G. Kachurovskii, “The rate of convergence in ergodic theorems”, Russian Math. Surveys, 51:4 (1996), 653–703
Citation in format AMSBIB
\Bibitem{Kac96}
\by A.~G.~Kachurovskii
\paper The rate of convergence in ergodic theorems
\jour Russian Math. Surveys
\yr 1996
\vol 51
\issue 4
\pages 653--703
\mathnet{http://mi.mathnet.ru/eng/rm995}
\crossref{https://doi.org/10.1070/RM1996v051n04ABEH002964}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1422228}
\zmath{https://zbmath.org/?q=an:0880.60024}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1996RuMaS..51..653K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996WJ45300002}
\elib{https://elibrary.ru/item.asp?id=13240322}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0030353041}
Linking options:
  • https://www.mathnet.ru/eng/rm995
  • https://doi.org/10.1070/RM1996v051n04ABEH002964
  • https://www.mathnet.ru/eng/rm/v51/i4/p73
  • This publication is cited in the following 117 articles:
    1. E. Sander, J. D. Meiss, “Proportions of incommensurate, resonant, and chaotic orbits for torus maps”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 35:1 (2025)  crossref
    2. Matthew J. Colbrook, Qin Li, Ryan V. Raut, Alex Townsend, “Beyond expectations: residual dynamic mode decomposition and variance for stochastic dynamical systems”, Nonlinear Dyn, 112:3 (2024), 2037  crossref
    3. Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira, Edson Souza, “On spectral measures and convergence rates in von Neumann's Ergodic theorem”, Monatsh Math, 203:3 (2024), 543  crossref
    4. Matthew J. Colbrook, Alex Townsend, “Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems”, Comm Pure Appl Math, 77:1 (2024), 221  crossref
    5. Christophe Zhang, Enrique Zuazua, “A quantitative analysis of Koopman operator methods for system identification and predictions”, Comptes Rendus. Mécanique, 351:S1 (2024), 721  crossref
    6. A. G. Kachurovskii, I. V. Podvigin, V. È. Todikov, A. Zh. Khakimbaev, “A Spectral Criterion for Power-Law Convergence Rate in the Ergodic Theorem for {𝕑}^{d}{𝕑}^{d} and {𝕉}^{d}{𝕉}^{d} Actions”, Sib Math J, 65:1 (2024), 76  crossref
    7. A. G. Kachurovskii, I. V. Podvigin, V. E. Todikov, A. Zh. Khakimbaev, “Spektralnyi kriterii stepennoi skorosti skhodimosti v ergodicheskoi teoreme dlya ZdRd deistvii”, Sib. matem. zhurn., 65:1 (2024), 92–114  mathnet  crossref
    8. I. V. Podvigin, “Kriterii stepennoi skorosti skhodimosti ergodicheskikh srednikh dlya unitarnykh deistvii grupp Zd i Rd”, Algebra i analiz, 36:4 (2024), 148–164  mathnet
    9. David Blessing, J. D. Mireles James, “Weighted Birkhoff Averages and the Parameterization Method”, SIAM J. Appl. Dyn. Syst., 23:3 (2024), 1766  crossref
    10. Matthew J. Colbrook, Handbook of Numerical Analysis, 25, Numerical Analysis Meets Machine Learning, 2024, 127  crossref
    11. Youri Davydov, Arkady Tempelman, “Randomized limit theorems for stationary ergodic random processes and fields”, Stochastic Processes and their Applications, 174 (2024), 104380  crossref
    12. Oscar F. Bandtlow, Wolfram Just, Julia Slipantschuk, “EDMD for expanding circle maps and their complex perturbations”, Applied and Computational Harmonic Analysis, 2024, 101690  crossref
    13. I. V. Podvigin, “On Convergence Rates in the Birkhoff Ergodic Theorem”, Sib Math J, 65:5 (2024), 1170  crossref
    14. I. V. Podvigin, “O skorostyakh skhodimosti v ergodicheskoi teoreme Birkgofa”, Sib. matem. zhurn., 65:5 (2024), 991–1010  mathnet  crossref
    15. M. Ruth, D. Bindel, “Finding Birkhoff averages via adaptive filtering”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:12 (2024)  crossref
    16. J.D. Meiss, E. Sander, “Resonance and weak chaos in quasiperiodically-forced circle maps”, Communications in Nonlinear Science and Numerical Simulation, 2024, 108562  crossref
    17. A. G. Kachurovskii, I. V. Podvigin, A. J. Khakimbaev, “Uniform Convergence on Subspaces in von Neumann Ergodic Theorem with Discrete Time”, Math. Notes, 113:5 (2023), 680–693  mathnet  crossref  crossref  mathscinet
    18. Russian Math. Surveys, 78:4 (2023), 635–777  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. A. G. Kachurovskii, I. V. Podvigin, V. E. Todikov, “Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time”, Sib. elektron. matem. izv., 20:1 (2023), 183–206  mathnet  crossref
    20. TERRY ADAMS, JOSEPH ROSENBLATT, “Existence and non-existence of solutions to the coboundary equation for measure-preserving systems”, Ergod. Th. Dynam. Sys., 43:7 (2023), 2137  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:2340
    Russian version PDF:1070
    English version PDF:123
    References:176
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025