## Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 3 (2019), 395-410.

### 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 $( X , G )$. 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.

#### Article information

Source
Involve, Volume 12, Number 3 (2019), 395-410.

Dates
Revised: 13 June 2017
Accepted: 25 June 2018
First available in Project Euclid: 5 February 2019

https://projecteuclid.org/euclid.involve/1549335629

Digital Object Identifier
doi:10.2140/involve.2019.12.395

Mathematical Reviews number (MathSciNet)
MR3905337

Zentralblatt MATH identifier
07033138

#### Citation

Medynets, Kostya; Talisse, James P. Toeplitz subshifts with trivial centralizers and positive entropy. Involve 12 (2019), no. 3, 395--410. doi:10.2140/involve.2019.12.395. https://projecteuclid.org/euclid.involve/1549335629

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