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  • Cited by 7
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    McGoff, Kevin and Pavlov, Ronnie 2016. Random $\mathbb{Z}^d$-shifts of finite type. Journal of Modern Dynamics, Vol. 10, Issue. 02, p. 287.

    PAVLOV, RONNIE 2014. A characterization of topologically completely positive entropy for shifts of finite type. Ergodic Theory and Dynamical Systems, Vol. 34, Issue. 06, p. 2054.

    PAVLOV, RONNIE 2011. Perturbations of multidimensional shifts of finite type. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 02, p. 483.

    Boyle, Mike and Schraudner, Michael 2009. shifts of finite type without equal entropy full shift factors. Journal of Difference Equations and Applications, Vol. 15, Issue. 1, p. 47.

    Hochman, Michael 2009. On the dynamics and recursive properties of multidimensional symbolic systems. Inventiones mathematicae, Vol. 176, Issue. 1, p. 131.

    BAN, JUNG-CHAO and CHANG, CHIH-HUNG 2008. ON THE DENSE ENTROPY OF TWO-DIMENSIONAL INHOMOGENEOUS CELLULAR NEURAL NETWORKS. International Journal of Bifurcation and Chaos, Vol. 18, Issue. 11, p. 3221.

    Desai, Angela 2006. Subsystem entropy for ℤd sofic shifts. Indagationes Mathematicae, Vol. 17, Issue. 3, p. 353.

  • Ergodic Theory and Dynamical Systems, Volume 23, Issue 4
  • August 2003, pp. 1227-1245

Entropy gaps and locally maximal entropy in $\mathbb{Z}^d$ subshifts

  • ANTHONY QUAS (a1) and AYŞE A. ŞAHİN (a2)
  • DOI:
  • Published online: 01 August 2003

In this paper, we study the behaviour of the entropy function of higher-dimensional shifts of finite type. We construct a topologically mixing $\mathbb{Z}^2$ shift of finite type whose ergodic invariant measures are connected in the $\overline{d}$ topology and whose entropy function has a strictly local maximum. We also construct a topologically mixing $\mathbb{Z}^2$ shift of finite type X with the property that there is a uniform gap between the topological entropy of X and the topological entropy of any subshift of X with stronger mixing properties. Our examples illustrate the necessity of strong topological mixing hypotheses in existing higher-dimensional representation and embedding theorems.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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