#### Vol. 12, No. 3, 2019

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Toeplitz subshifts with trivial centralizers and positive entropy

### Kostya Medynets and James P. Talisse

Vol. 12 (2019), No. 3, 395–410
##### Abstract

Given a dynamical system $\left(X,G\right)$, the centralizer $C\left(G\right)$ denotes the group of all homeomorphisms of $X$ which commute with the action of $G$. This group is sometimes called the automorphism group of the dynamical system $\left(X,G\right)$. We generalize the construction of Bułatek and Kwiatkowski (1992) to ${ℤ}^{d}$-Toeplitz systems by identifying a class of ${ℤ}^{d}$-Toeplitz systems that have trivial centralizers. We show that this class of ${ℤ}^{d}$-Toeplitz systems with trivial centralizers contains systems with positive topological entropy.

##### Keywords
topological dynamics, symbolic dynamics, automorphism group, centralizer, topological entropy
##### Mathematical Subject Classification 2010
Primary: 37B05, 37B40, 37B50