Isomorphic extensions and applications

By Tomasz Downarowicz, Eli Glasner. 2015

73 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1462befb2d2f66698724d04ecbf6b78a8c010ece

How researchers see this paper

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In Computational Theory and Mathematics

1. David Kerr
2. G'abor Szab'o
3. Ben Hayes
4. Xiangdong Ye
5. Eli Glasner
6. Jian Li

In Geometry and Topology

1. David Kerr
2. G'abor Szab'o
3. Hanfeng Li
4. Xiangdong Ye
5. Eli Glasner
6. Frederic Pierre Jean Latrémolière
7. A. Kavruk
8. Wen Huang

In Mathematical Physics

1. David Kerr
2. G'abor Szab'o
3. Hanfeng Li
4. Ben Hayes
5. Xiangdong Ye
6. Eli Glasner
7. Frederic Pierre Jean Latrémolière
8. Wen Huang

Citations in the corpus

• Almost Finiteness and the Small Boundary Property (2018, background): “s measure-isomorphic over singleton fibres then it is measure-isomorphic, as π restricts to a G-equivariant Borel isomorphism π−1(Sπ) → Sπ ([20], Corollary 15.2). The converse is false, as examples in [9] demonstrate. The following is immediate from Proposition 4.1. Proposition 4.3. For the extension”