On the automorphism group of minimal S-adic subshifts of finite alphabet rank

Bastián Espinoza (1, 2) , Alejandro Maass (2, 3)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
3 CMM - Center for Mathematical Modeling

It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the automorphism group of a minimal S-adic subshift of finite alphabet rank is virtually $\mathbb{Z}$. The proof is based on a fine combinatorial analysis of the asymptotic classes in this type of subshifts, which we prove are a finite number.

Mots clés: May 13; 2021. 2020 Mathematics Subject Classification. Primary: 37B10; Secondary: 37B10 S-adic subshifts; automorphism group; minimal Cantor systems; finite topological rank

Domaines: Systèmes dynamiques [math.DS]

Bastián Espinoza, Alejandro Maass. On the automorphism group of minimal S-adic subshifts of finite alphabet rank. 2022. ⟨hal-03585476⟩