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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2022

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

#### Résumé

Abstract It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb {Z}$ [Cyr and Kra. The automorphism group of a shift of linear growth: beyond transitivity. Forum Math. Sigma 3 (2015), e5; Donoso et al . On automorphism groups of low complexity subshifts. Ergod. Th. & Dynam. Sys. 36 (1) (2016), 64–95]. In this article we extend this result to a broader class proving that the automorphism group of a minimal $\mathcal {S}$ -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.

#### Domaines

Mathématiques [math]

### Dates et versions

hal-04010512 , version 1 (01-03-2023)

### Identifiants

• HAL Id : hal-04010512 , version 1
• DOI :

### Citer

Bastián Espinoza, Alejandro Maass. On the automorphism group of minimal -adic subshifts of finite alphabet rank. Ergodic Theory and Dynamical Systems, 2022, 42 (9), pp.2800-2822. ⟨10.1017/etds.2021.64⟩. ⟨hal-04010512⟩

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