Concepedia

Birkhoff Ergodic Theorem

The Birkhoff Ergodic Theorem is a fundamental result in ergodic theory, within dynamical systems, that establishes the almost everywhere equality between the time average and the space average of an integrable function under a measure-preserving transformation.

218

Publications

9.7K

Citations

309

Authors

220

Institutions

Publications per year

2017–2026

19

Variants

Birkhoff's Ergodic TheoremIndividual Ergodic Theorem

Parents

Publications

218

Representations for real numbers and their ergodic properties

A. Rényi · Acta Mathematica Academiae Scientiarum Hungaricae · 1957 · 1.2K citations

, , +10

Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator

SIAM Journal on Applied Dynamical Systems · 2017 · 451 citations · Full text

, , +16

AN INTRODUCTION TO ERGODIC THEORY (Graduate Texts in Mathematics, 79)

D. Newton · Bulletin of the London Mathematical Society · 1982 · 358 citations

, , +14

The Birkhoff theorem for finite algebras

Jan Reiterman · Algebra Universalis · 1982 · 215 citations

, , +11

An Improved Subadditive Ergodic Theorem

Thomas M. Liggett · The Annals of Probability · 1985 · 209 citations · Full text

, , +14

1–5 of 218

Authors

309

  1. DN
    D. Newton

    University of Sussex, United Kingdom

    4 publications · 631 citations

    4

    h-index

  2. AG
    A. G. Kachurovskiĭ

    Russian Academy of Sciences, Russia

    3 publications · 36 citations

    3

    h-index

  3. MH
    Mathieu Hoyrup

    Institut national de recherche en sciences et technologies du numérique, France

    3 publications · 78 citations

    3

    h-index

  4. IV
    I. V. Podvigin

    Novosibirsk State University, Russia

    3 publications · 57 citations

    3

    h-index

  5. JA
    Jon Aaronson

    Tel Aviv University, Israel

    3 publications · 111 citations

    3

    h-index

1–5 of 309

Institutions

220

  1. Centre National de la Recherche Scientifique

    Paris, France

    11 h-index

    13 publications

    460 citations

  2. Russian Academy of Sciences

    Moscow, Russia

    5 h-index

    6 publications

    139 citations

  3. Tel Aviv University

    Tel Aviv, Israel

    5 h-index

    6 publications

    241 citations

  4. University of California, Berkeley

    Berkeley, United States

    5 h-index

    5 publications

    254 citations

  5. University of Bristol

    Bristol, United Kingdom

    4 h-index

    5 publications

    110 citations

  6. Hebrew University of Jerusalem

    Jerusalem, Israel

    4 h-index

    4 publications

    133 citations

  7. Mathematical Institute of the Slovak Academy of Sciences

    Bratislava, Slovakia

    3 h-index

    4 publications

    166 citations

  8. Institute for Information Transmission Problems

    Moscow, Russia

    3 h-index

    3 publications

    146 citations

1–8 of 220

Venues

  1. Communications in Mathematical Physics

    10 publications · 558 citations

    10

    h-index

  2. Bulletin of the London Mathematical Society

    10 publications · 961 citations

    10

    h-index

  3. Israel Journal of Mathematics

    8 publications · 287 citations

    8

    h-index

  4. Ergodic Theory and Dynamical Systems

    7 publications · 215 citations

    7

    h-index

  5. Journal of Functional Analysis

    7 publications · 253 citations

    7

    h-index

1–5