\(\mathbb Z^d\) Toeplitz arrays
type: Item
instance of: scholarly article
title: \(\mathbb Z^d\) Toeplitz arrays
zbMATH Open document ID: 1130.54016
author: María Isabel Cortez
published in: Discrete and Continuous Dynamical Systems
publication date: 2007-04-05T00:00:00Z
review text: In the paper under review the definitions of odometer and Toeplitz flow are extended to \(\mathbb Z^d\) actions \((d\geq 1)\); the special cases \(d=1,2\) were considered before in [\textit{K. Jacobs} and \textit{M. Keane}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 13, 123-131 (1969; Zbl 0195.52703)] and [\textit{T. Downarowicz}, Isr. J. Math. 97, 239-251 (1997; Zbl 0893.54032)], respectively. The main result is the characterization of \(\mathbb Z^d\)-regularly systems as the minimal almost 1-1 extensions of odometers and the \(\mathbb Z^d\)-Toeplitz systems as the family of subshifts which are regularly recurrent. Moreover two interesting \(\mathbb Z^2\)-Toeplitz flows are constructed: the first one with a finite number of ergodic mesures and the second one being uniquely ergodic with positive entropy.
reviewed by: Gabriel Soler López
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B50
zbMATH DE Number: 5140554
zbMATH Keywords: Almost 1-1 extensions
zbMATH Keywords: Toeplitz
zbMATH Keywords: odometer
MaRDI profile type: Publication
full work available at URL: dcds.2006.15.859
OpenAlex ID: W2034683933
DOI: 10.3934/DCDS.2006.15.859
description: scientific article; zbMATH DE number 5140554