Isomorphic extensions and applications

Tomasz Downarowicz, Eli Glasner

Research output: Contribution to journalArticlepeer-review

Abstract

If π:(X,T)→(Z,S) is a topological factor map between uniquely ergodic topological dynamical systems, then (X,T) is called an isomorphic extension of (Z,S) if π is also a measure-theoretic isomorphism. We consider the case when the systems are minimal and we pay special attention to equicontinuous (Z,S). We first establish a characterization of this type of isomorphic extensions in terms of mean equicontinuity, and then show that an isomorphic extension need not be almost one-to-one, answering questions of Li, Tu and Ye.

Original languageEnglish
Pages (from-to)321-338
Number of pages18
JournalTopological Methods in Nonlinear Analysis
Volume48
Issue number1
DOIs
StatePublished - Sep 2016

Keywords

  • Almost oneto-one extension
  • Isomorphic extension
  • Mean equicontinuity
  • Minimality
  • Skew product
  • Unique ergodicity

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