Ergodicity and weak-mixing of homogeneous extensions of measure-preserving transformations with applications to Markov shifts

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6 Citations (Scopus)

Abstract

Given a homogeneous extension S′ of a measure-preserving transformation T, we provide necessary and sufficient conditions for the ergodicity and weak-mixing of S′ in terms of functional equations. We then apply our findings to the case when T is a Markov shift and the associated skewing function of S′ depends on a finite number of coordinates. In this case, we obtain a simplification to the appropriate functional equations.

Original languageEnglish
Pages (from-to)149-170
Number of pages22
JournalMonatshefte fur Mathematik
Volume123
Issue number2
Publication statusPublished - 1997

Fingerprint

Weak Mixing
Measure-preserving Transformations
Ergodicity
Functional equation
Simplification
Necessary Conditions
Sufficient Conditions

Keywords

  • Ergodicity
  • Homogeneous extensions
  • Markov shifts
  • Measure-preserving transformations
  • Weak-mixing

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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AB - Given a homogeneous extension S′ of a measure-preserving transformation T, we provide necessary and sufficient conditions for the ergodicity and weak-mixing of S′ in terms of functional equations. We then apply our findings to the case when T is a Markov shift and the associated skewing function of S′ depends on a finite number of coordinates. In this case, we obtain a simplification to the appropriate functional equations.

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KW - Markov shifts

KW - Measure-preserving transformations

KW - Weak-mixing

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