Vol. 12, No. 3, 2019

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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
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 d-Toeplitz systems by identifying a class of d-Toeplitz systems that have trivial centralizers. We show that this class of d-Toeplitz systems with trivial centralizers contains systems with positive topological entropy.

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