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arXiv · 1502.06999

Isomorphic extensions and applications

Tomasz Downarowicz·Eli Glasner
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Abstract

If $\pi:(X,T)\to(Z,S)$ 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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Tomasz Downarowicz, Eli Glasner. 2015-02-24. Isomorphic extensions and applications. https://arxiv.org/abs/1502.06999

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