Monotone equivalence in ergodic theory

Anatoly Katok

Research output: Contribution to journalArticle

7 Citations (Scopus)

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

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Ergodic Theory
Automorphisms
Monotone
Equivalence
Discrete Spectrum
Asymptotic Properties
Coding
Entropy
Partition
Trajectory
Necessary Conditions
Invariant
Sufficient Conditions
Zero
Approximation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Katok, Anatoly. / Monotone equivalence in ergodic theory. In: Mathematics of the USSR - Izvestija. 1977 ; Vol. 11, No. 1. pp. 99-146.
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Monotone equivalence in ergodic theory. / Katok, Anatoly.

In: Mathematics of the USSR - Izvestija, Vol. 11, No. 1, 28.02.1977, p. 99-146.

Research output: Contribution to journalArticle

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