Toeplitz Subshifts with Trivial Centralizers and Positive Entropy

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.

REU project, 15 pages