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Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers

Volume 147 / 2017

Mieczysław K. Mentzen Colloquium Mathematicum 147 (2017), 87-94 MSC: Primary 37B05; Secondary 37B10. DOI: 10.4064/cm6927-5-2016 Published online: 9 December 2016

Abstract

We prove that for the subshifts defined by the sets of $\mathcal {B}$-free numbers, where $\sum _{b\in \mathcal {B}}{1/b} \lt \infty $ and the elements of $\mathcal {B}$ are pairwise coprime, the set of homeomorphisms commuting with the shift $T$ is trivial, i.e. $\operatorname {Aut}\nolimits (T)=\{T^n:n\in \mathbb {Z}\}$.

Authors

  • Mieczysław K. MentzenFaculty of Mathematics and Computer Science
    Nicholas Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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