1 results
On the automorphism group of minimal
$\mathcal {S}$
-adic subshifts of finite alphabet rank
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 9 / September 2022
- Published online by Cambridge University Press:
- 30 June 2021, pp. 2800-2822
- Print publication:
- September 2022
-
- Article
- Export citation
-
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. Sigma3 (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.
