Dynamical properties of minimal Ferenczi subshifts

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