# American Institute of Mathematical Sciences

August  2006, 15(3): 859-881. doi: 10.3934/dcds.2006.15.859

## $Z^d$ Toeplitz arrays

 1 Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile

Received  January 2005 Revised  November 2005 Published  April 2006

In this paper we give a definition of Toeplitz sequences and odometers for $\mathbb{Z}^d$ actions for $d\geq 1$ which generalizes that in dimension one. For these new concepts we study properties of the induced Toeplitz dynamical systems and odometers classical for $d=1$. In particular, we characterize the $\mathbb{Z}^d$-regularly recurrent 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.
Citation: María Isabel Cortez. $Z^d$ Toeplitz arrays. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 859-881. doi: 10.3934/dcds.2006.15.859
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