Dynamical properties of minimal Ferenczi subshifts

TL;DR

This paper introduces Ferenczi subshifts, a class of rank one subshifts with bounded spacers, and analyzes their dynamical properties including topological rank, orbit equivalence, and eigenvalues.

Contribution

It provides an explicit S-adic representation for Ferenczi subshifts and studies their dynamical behavior, including spectral properties and induced systems.

Findings

Ferenczi subshifts have a well-defined topological rank.

They possess an induced Toeplitz subshift with discrete spectrum.

The paper characterizes continuous and non-continuous eigenvalues.

Abstract

We provide an explicit S-adic representation of rank one subshifts with bounded spacers and call the subshifts obtained in this way ''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 systems that is a Toeplitz subshift having discrete spectrum. We also characterize continuous and non continuous eigenvalues of minimal Ferenczi subshifts.