Monotone equivalence in ergodic theory

Anatoly Katok

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9 Scopus citations

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 #x201C;words” arising from a coding of most trajectories by a finite partition. Also certain monotone invariants are defined and their properties discussed.

Original languageEnglish (US)
Pages (from-to)99-146
Number of pages48
JournalMathematics of the USSR - Izvestija
Volume11
Issue number1
DOIs
StatePublished - Feb 28 1977

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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