Toeplitz subshifts with trivial centralizers and positive entropy

Medynets, Kostya; Talisse, James P.

doi:10.2140/involve.2019.12.395

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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

DOI: 10.2140/involve.2019.12.395

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.

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Keywords

topological dynamics, symbolic dynamics, automorphism group, centralizer, topological entropy

Mathematical Subject Classification 2010

Primary: 37B05, 37B40, 37B50

Milestones

Received: 3 May 2017

Revised: 13 June 2017

Accepted: 25 June 2018

Published: 14 December 2018

Communicated by David Royal Larson

Authors

Kostya Medynets
Mathematics Department United States Naval Academy Annapolis, MD United States

James P. Talisse
Mathematics Department United States Naval Academy Annapolis, MD United States

Vol. 12, No. 3, 2019