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Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 1, Pages 99–146
DOI: https://doi.org/10.1070/IM1977v011n01ABEH001696 (Mi im1794) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Monotone equivalence in ergodic theory

A. B. Katok
English version PDF (2165 kB) Citations (21) Russian version article
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DOI: https://doi.org/10.1070/IM1977v011n01ABEH001696
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.
Received: 02.03.1976
Bibliographic databases:
UDC: 517.9+513.88
MSC: 28A65
Language: English
Original paper language: Russian
Citation: A. B. Katok, “Monotone equivalence in ergodic theory”, Math. USSR-Izv., 11:1 (1977), 99–146
Citation in format AMSBIB
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\by A.~B.~Katok
\paper Monotone equivalence in ergodic theory
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\yr 1977
\vol 11
\issue 1
\pages 99--146
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    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:516
    Russian version PDF:202
    English version PDF:30
    References:68
    First page:3
     
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