We provide an explicit $\mathcal {S}$-adic representation of rank-one subshifts with bounded spacers and call the subshifts obtained in this way ‘minimal Ferenczi subshifts’. We aim to show that this approach is very convenient to study the dynamical behavior of rank-one systems. For instance, we compute their topological rank, the strong and the weak orbit equivalence class. We observe that they have an induced system that is a Toeplitz subshift having discrete spectrum. We also characterize continuous and non-continuous eigenvalues of minimal Ferenczi subshifts.

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.