Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers
Volume 147 / 2017
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. $\operatorname {Aut}\nolimits (T)=\{T^n:n\in \mathbb {Z}\}$.
