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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 1, Pages 104–157 (Mi izv1794)  

This article is cited in 8 scientific papers (total in 8 papers)

Monotone equivalence in ergodic theory

A. B. Katok


Abstract: A class of monotonely equivalent automorphisms (standard automorphisms), which includes all ergodic automorphisms with discrete spectrum and most of the well-known examples of automorphisms with zero entropy, is studied. The basic results are two necessary and sufficient conditions for standardness: the first in terms of periodic approximation and the second in terms of the asymptotic properties of “words” arising from a coding of most trajectories by a finite partition. Also certain monotone invariants are defined and their properties discussed.
Bibliography: 36 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:1, 99–146

Bibliographic databases:

UDC: 517.9+513.88
MSC: 28A65
Received: 02.03.1976

Citation: A. B. Katok, “Monotone equivalence in ergodic theory”, Izv. Akad. Nauk SSSR Ser. Mat., 41:1 (1977), 104–157; Math. USSR-Izv., 11:1 (1977), 99–146

Citation in format AMSBIB
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\paper Monotone equivalence in ergodic theory
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\yr 1977
\vol 41
\issue 1
\pages 104--157
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\vol 11
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\pages 99--146
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Sataev, “An invariant of monotone equivalence determining the quotients of automorphisms monotonely equivalent to a Bernoulli shift”, Math. USSR-Izv., 11:1 (1977), 147–169  mathnet  crossref  mathscinet  zmath
    2. Marlies Gerber, “A zero-entropy mixing transformation whose product with itself is loosely Bernoulli”, Isr J Math, 38:1-2 (1981), 1  crossref  mathscinet  zmath  isi
    3. A. M. Vershik, “Dynamic theory of growth in groups: Entropy, boundaries, examples”, Russian Math. Surveys, 55:4 (2000), 667–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. B. R. Fayad, A. B. Katok, A. Windsor, “Mixed spectrum reparameterizations of linear flows on $\mathbb T^2$”, Mosc. Math. J., 1:4 (2001), 521–537  mathnet  mathscinet  zmath  elib
    5. Fraczek K., Kulaga-Przymus J., Lemanczyk M., “Non-reversibility and self-joinings of higher orders for ergodic flows”, J. Anal. Math., 122 (2014), 163–227  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. A. M. Vershik, P. B. Zatitskii, “Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph”, Funct. Anal. Appl., 52:4 (2018), 258–269  mathnet  crossref  crossref  isi  elib
    8. Kanigowski A., Hertz F.R., Vinhage K., “On the Non-Equivalence of the Bernoulli and K Properties in Dimension Four”, J. Mod. Dyn., 13 (2018), 221–250  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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