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arXiv · 1706.05632

Toeplitz Subshifts with Trivial Centralizers and Positive Entropy

Kostya Medynets·James P. Talisse
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Abstract

Given a dynamical system $(X,G)$, the centralizer $C(G)$ 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 $(X,G)$. In this note, we generalize the construction of Bulatek and Kwiatkowski (1992) to $\mathbb Z^d$-Toepltiz systems by identifying a class of $\mathbb Z^d$-Toeplitz systems that have trivial centralizers. We show that this class of $\mathbb Z^d$-Toeplitz with trivial centralizers contains systems with positive topological entropy.

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Kostya Medynets, James P. Talisse. 2017-06-18. Toeplitz Subshifts with Trivial Centralizers and Positive Entropy. https://arxiv.org/abs/1706.05632

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