American Institute of Mathematical Sciences

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

$Z^d$ Toeplitz arrays

María Isabel Cortez 1,

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.
Keywords: odometer., Toeplitz, Almost 1-1 extensions, tiling.
Mathematics Subject Classification: Primary: 54H20; Secondary: 37B5.
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
[1]

Yong Xia, Yu-Jun Gong, Sheng-Nan Han. A new semidefinite relaxation for $L_{1}$-constrained quadratic optimization and extensions. Numerical Algebra, Control and Optimization, 2015, 5 (2) : 185-195. doi: 10.3934/naco.2015.5.185
[2]

Alexei Kaltchenko, Nina Timofeeva. Entropy estimators with almost sure convergence and an O(n-1) variance. Advances in Mathematics of Communications, 2008, 2 (1) : 1-13. doi: 10.3934/amc.2008.2.1
[3]

A. Alexandrou Himonas, Gerson Petronilho. A $ G^{\delta, 1} $ almost conservation law for mCH and the evolution of its radius of spatial analyticity. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2031-2050. doi: 10.3934/dcds.2020351
[4]

Caiyan Li, Dongsheng Li. $ W^{1,p} $ estimates for elliptic systems on composite material with almost partially BMO coefficients. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3143-3159. doi: 10.3934/cpaa.2021100
[5]

Motserrat Corbera, Jaume Llibre, Claudia Valls. Periodic orbits of perturbed non-axially symmetric potentials in 1:1:1 and 1:1:2 resonances. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2299-2337. doi: 10.3934/dcdsb.2018101
[6]

Fatma Gamze Düzgün, Ugo Gianazza, Vincenzo Vespri. $1$-dimensional Harnack estimates. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 675-685. doi: 10.3934/dcdss.2016021
[7]

Agust Sverrir Egilsson. On embedding the $1:1:2$ resonance space in a Poisson manifold. Electronic Research Announcements, 1995, 1: 48-56.

[8]

Mikko Salo. Stability for solutions of wave equations with $C^{1,1}$ coefficients. Inverse Problems and Imaging, 2007, 1 (3) : 537-556. doi: 10.3934/ipi.2007.1.537
[9]

Rodolfo Acuňa-Soto, Luis Castaňeda-Davila, Gerardo Chowell. A perspective on the 2009 A/H1N1 influenza pandemic in Mexico. Mathematical Biosciences & Engineering, 2011, 8 (1) : 223-238. doi: 10.3934/mbe.2011.8.223
[10]

Jelena Rupčić. Convergence of lacunary SU(1, 1)-valued trigonometric products. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1275-1289. doi: 10.3934/cpaa.2020062
[11]

Keonhee Lee, Kazumine Moriyasu, Kazuhiro Sakai. $C^1$-stable shadowing diffeomorphisms. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 683-697. doi: 10.3934/dcds.2008.22.683
[12]

Lan Wen. A uniform $C^1$ connecting lemma. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 257-265. doi: 10.3934/dcds.2002.8.257
[13]

Stephen C. Preston, Ralph Saxton. An $H^1$ model for inextensible strings. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2065-2083. doi: 10.3934/dcds.2013.33.2065
[14]

R.D.S. Oliveira, F. Tari. On pairs of differential $1$-forms in the plane. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 519-536. doi: 10.3934/dcds.2000.6.519
[15]

Lori Alvin. Toeplitz kneading sequences and adding machines. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3277-3287. doi: 10.3934/dcds.2013.33.3277
[16]

Huimin Zheng, Xuejun Guo, Hourong Qin. The Mahler measure of $ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $. Electronic Research Archive, 2020, 28 (1) : 103-125. doi: 10.3934/era.2020007
[17]

Braxton Osting, Jérôme Darbon, Stanley Osher. Statistical ranking using the $l^{1}$-norm on graphs. Inverse Problems and Imaging, 2013, 7 (3) : 907-926. doi: 10.3934/ipi.2013.7.907
[18]

Nikolaz Gourmelon. Generation of homoclinic tangencies by $C^1$-perturbations. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 1-42. doi: 10.3934/dcds.2010.26.1
[19]

Flavio Abdenur, Lorenzo J. Díaz. Pseudo-orbit shadowing in the $C^1$ topology. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 223-245. doi: 10.3934/dcds.2007.17.223
[20]

Yu. Dabaghian, R. V. Jensen, R. Blümel. Integrability in 1D quantum chaos. Conference Publications, 2003, 2003 (Special) : 206-212. doi: 10.3934/proc.2003.2003.206

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (314)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy