Involve: A Journal of Mathematics

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

Toeplitz subshifts with trivial centralizers and positive entropy

Kostya Medynets and James P. Talisse

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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.

Article information

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

Received: 3 May 2017
Revised: 13 June 2017
Accepted: 25 June 2018
First available in Project Euclid: 5 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37B40: Topological entropy 37B50: Multi-dimensional shifts of finite type, tiling dynamics

topological dynamics symbolic dynamics automorphism group centralizer topological entropy


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.

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