Geodesic
On automorphism groups of Toeplitz subshifts
Discrete analysis (2017) Cet article a éte moissonné depuis la source Scholastica

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In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non superlinear, we prove that the automorphism group is, modulo a finite cyclic group, generated by a unique root of the shift. In the subquadratic complexity case, we show that the automorphism group modulo the torsion is generated by the roots of the shift map and that the result of the non superlinear case is optimal. Namely, for any $\varepsilon > 0$ we construct examples of minimal Toeplitz subshifts with complexity bounded by $C n^{1+ε}$ whose automorphism groups are not finitely generated. Finally, we observe the coalescence and the automorphism group give no restriction on the complexity since we provide a family of coalescent Toeplitz subshifts with positive entropy such that their automorphism groups are arbitrary finitely generated infinite abelian groups with cyclic torsion subgroup (eventually restricted to powers of the shift).
Publié le : 
@article{DAS_2017_a9,
     author = {Sebasti\'an Donoso and Fabien Durand and Alejandro Maass and Samuel Petite},
     title = {On automorphism groups of {Toeplitz} subshifts},
     journal = {Discrete analysis},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2017_a9/}
}
TY  - JOUR
AU  - Sebastián Donoso
AU  - Fabien Durand
AU  - Alejandro Maass
AU  - Samuel Petite
TI  - On automorphism groups of Toeplitz subshifts
JO  - Discrete analysis
PY  - 2017
UR  - http://geodesic.mathdoc.fr/item/DAS_2017_a9/
LA  - en
ID  - DAS_2017_a9
ER  - 
%0 Journal Article
%A Sebastián Donoso
%A Fabien Durand
%A Alejandro Maass
%A Samuel Petite
%T On automorphism groups of Toeplitz subshifts
%J Discrete analysis
%D 2017
%U http://geodesic.mathdoc.fr/item/DAS_2017_a9/
%G en
%F DAS_2017_a9
Sebastián Donoso; Fabien Durand; Alejandro Maass; Samuel Petite. On automorphism groups of Toeplitz subshifts. Discrete analysis (2017). http://geodesic.mathdoc.fr/item/DAS_2017_a9/