Measurable rigidity of algebraic \(\mathbb{Z}^d\)-actions (Q2778791)
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scientific article; zbMATH DE number 1722419
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Measurable rigidity of algebraic \(\mathbb{Z}^d\)-actions |
scientific article; zbMATH DE number 1722419 |
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27 September 2002
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rigidity
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commuting automorphisms
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Measurable rigidity of algebraic \(\mathbb{Z}^d\)-actions (English)
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This paper surveys the recent rigidity results proving that measurable conjugacies between irreducible mixing expansive \(\mathbb Z^d\)-actions by automorphisms of compact abelian groups must be affine maps, due to the author and \textit{B. Kitchens} [Invent. Math. 142, 559-577 (2000; Zbl 0970.22006)] and the author, \textit{A. Katok} and \textit{S. Katok} [``Rigidity of measurable structure for \(Z^d\)-actions by automorphisms of a torus'', Preprint, \url{http://www.esi.ac.at/Preprint-shadows/esi850.html}]. The proofs of the two main cases (connected and zero-dimensional groups) are sketched, and several illuminating examples are given.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00044].
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