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Dynamical properties of minimal Ferenczi subshifts

Published online by Cambridge University Press:  22 February 2023

Laboratoire Amiénois de Mathématique Fondamentale et Apliquée, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens cedex 1, France (e-mail:
Laboratoire Amiénois de Mathématique Fondamentale et Apliquée, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens cedex 1, France (e-mail:


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.

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© The Author(s), 2023. Published by Cambridge University Press

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