A dynamical system with a \(Z^ 2\) centralizer
type: Item
instance of: scholarly article
title: A dynamical system with a \(Z^ 2\) centralizer
zbMATH Open document ID: 0883.28015
author: Kyewon K. Park
author: Aimee S. A. Johnson
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-11-30T00:00:00Z
review text: The paper is concerned with Chacon \(\mathbb{Z}^2\) actions. The purpose of the authors is to study the particular action of the nontrivial subgroup \(\mathbb{Z}\) of \(\mathbb{Z}^2\). They describe the prototypical example of a Chacon \(\mathbb{Z}^2\) action and develop a symbolic version of its construction. Denoting Chacon \(\mathbb{Z}^2\) action by \(\{T^iS^j\mid(i,j)\in\mathbb{Z}^2\}\), the authors give attention to its study in terms of \(T\). Two main results are obtained: -- If \(P\) is the time zero partition of \(X\subset\{0,1\}^{\mathbb{Z}^2}\), then \(P\) is a generating partition under \(T\). -- The centralizer of \(T\) is the \(\mathbb{Z}^2\) group \(\{T^iS^j\mid(i,j)\in\mathbb{Z}^2\}\).
Mathematics Subject Classification ID: 28D15
zbMATH DE Number: 1031652
zbMATH Keywords: Chacon \(\mathbb{Z}^ 2\) actions
reviewed by: Emilia Petrisor
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5407
OpenAlex ID: W2053325940
cites work: Chacon's automorphism has minimal self joinings
cites work: Ensemble d'invariants pour les produits croisés de Anzai
cites work: The joinings within a class of \({\mathbb{Z}{}}^ 2\)-actions
cites work: An example of a measure preserving map with minimal self-joinings, and applications
DOI: 10.1006/JMAA.1997.5407
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description: scientific article; zbMATH DE number 1031652