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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.
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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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http://mi.mathnet.ru/eng/izv1794 http://mi.mathnet.ru/eng/izv/v41/i1/p104
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This publication is cited in the following articles:
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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
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Marlies Gerber, “A zero-entropy mixing transformation whose product with itself is loosely Bernoulli”, Isr J Math, 38:1-2 (1981), 1
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A. M. Vershik, “Dynamic theory of growth in groups: Entropy, boundaries, examples”, Russian Math. Surveys, 55:4 (2000), 667–733
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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
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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
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A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
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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
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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
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