Topological Methods in Nonlinear Analysis

Isomorphic extensions and applications

Tomasz Downarowicz and Eli Glasner

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If $\pi\colon (X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\pi$ 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.

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Topol. Methods Nonlinear Anal., Volume 48, Number 1 (2016), 321-338.

First available in Project Euclid: 30 September 2016

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Downarowicz, Tomasz; Glasner, Eli. Isomorphic extensions and applications. Topol. Methods Nonlinear Anal. 48 (2016), no. 1, 321--338. doi:10.12775/TMNA.2016.050.

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