Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers
Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 87-94
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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. $\operatorname {Aut}\nolimits (T)=\{T^n:n\in \mathbb {Z}\}$.
Keywords:
prove subshifts defined sets mathcal free numbers where sum mathcal infty elements mathcal pairwise coprime set homeomorphisms commuting shift trivial operatorname aut nolimits mathbb
Affiliations des auteurs :
Mieczysław K. Mentzen 1
@article{10_4064_cm6927_5_2016,
author = {Mieczys{\l}aw K. Mentzen},
title = {Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers},
journal = {Colloquium Mathematicum},
pages = {87--94},
publisher = {mathdoc},
volume = {147},
number = {1},
year = {2017},
doi = {10.4064/cm6927-5-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6927-5-2016/}
}
TY - JOUR
AU - Mieczysław K. Mentzen
TI - Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers
JO - Colloquium Mathematicum
PY - 2017
SP - 87
EP - 94
VL - 147
IS - 1
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm6927-5-2016/
DO - 10.4064/cm6927-5-2016
LA - en
ID - 10_4064_cm6927_5_2016
ER -
%0 Journal Article
%A Mieczysław K. Mentzen
%T Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers
%J Colloquium Mathematicum
%D 2017
%P 87-94
%V 147
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm6927-5-2016/
%R 10.4064/cm6927-5-2016
%G en
%F 10_4064_cm6927_5_2016
Mieczysław K. Mentzen. Automorphisms of subshifts defined by $\mathcal {B}$-free sets of integers. Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 87-94. doi: 10.4064/cm6927-5-2016
Cité par Sources :