Mathematics of the USSR-Izvestiya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find




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

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)
References:
PDF
HTML
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1977, Volume 41, Issue 1, Pages 104–157
Bibliographic databases:
UDC: 517.9+513.88
MSC: 28A65
Language: English
Original paper language: Russian
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
\Bibitem{Kat77}
\by A.~B.~Katok
\paper Monotone equivalence in ergodic theory
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 1
\pages 104--157
\mathnet{http://mi.mathnet.ru/im1794}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=442195}
\zmath{https://zbmath.org/?q=an:0372.28020|0379.28008}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 1
\pages 99--146
\crossref{https://doi.org/10.1070/IM1977v011n01ABEH001696}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977FB84400004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0010850931}
Linking options:
  • https://www.mathnet.ru/eng/im1794
  • https://doi.org/10.1070/IM1977v011n01ABEH001696
  • https://www.mathnet.ru/eng/im/v41/i1/p104
    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:504
    Russian version PDF:199
    English version PDF:24
    References:63
    First page:3
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024