Toeplitz Subshifts with Trivial Centralizers and Positive Entropy

2017/06/18 by Kostya Medynets, Medynets, Kostya, James P. Talisse +1
Mathematics · #37B05 #37B40 #37B50 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37B05 #msc:37B40 #msc:37B50

paper · pdf · doi:10.48550/arxiv.1706.05632

REU project, 15 pages

arxiv created 2017/06/18 · arxiv updated 2017/06/20

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.

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