Monotone equivalence in ergodic theory

Anatoly Katok

doi:10.1070/IM1977v011n01ABEH001696

Monotone equivalence in ergodic theory

Anatoly Katok

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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 language	English (US)
Pages (from-to)	99-146
Number of pages	48
Journal	Mathematics of the USSR - Izvestija
Volume	11
Issue number	1
DOIs	https://doi.org/10.1070/IM1977v011n01ABEH001696
State	Published - Feb 28 1977

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1070/IM1977v011n01ABEH001696

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AB - 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.

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Monotone equivalence in ergodic theory

Abstract

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