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

Abstract

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.