# Toeplitz Subshifts with Trivial Centralizers and Positive Entropy

## TL;DR

This paper constructs a class of $\\mathbb{Z}^d$-Toeplitz dynamical systems with trivial automorphism groups that also exhibit positive topological entropy, expanding understanding of their structural complexity.

## Contribution

It generalizes previous constructions to higher dimensions, identifying $\\mathbb{Z}^d$-Toeplitz systems with trivial centralizers and positive entropy.

## Key findings

- Identified a class of $\\mathbb{Z}^d$-Toeplitz systems with trivial centralizers.
- Showed these systems can have positive topological 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.