This paper offers several approaches to odometers (ie, adding machines) as dynamical
systems, and to their minimal almost 1-1 extensions (with both invertible and non-invertible …

We construct Bratteli–Vershik models for Toeplitz flows and characterize a class of properly
ordered Bratteli diagrams corresponding to these flows. We use this result to extend by a …

Recurrent–wandering, conservative–dissipative, contracting–expanding, deterministic–
chaotic, isometric–mixing, periodic–turbulent, distal–proximal, the list can go on and on …

In this paper we recall the concepts of G-odometers and G-subodometers for G-actions,
where G is a discrete finitely generated group; these generalize the notion of an odometer in …

Although Sarnak's conjecture holds for compact group rotations (irrational rotations,
odometers), it is not even known whether it holds for all Jewett-Krieger models of such …

In this paper we give a definition of Toeplitz sequences and odometers for Zd actions for d≥
1 which generalizes that in dimension one. For these new concepts we study properties of …

Let G be a countable residually finite group (for instance, endowed with the Haar measure.
The construction we propose is general (for amenable and non-amenable residually finite …

In this work we study $ S $-adic shifts generated by sequences of morphisms that are
constant-length. We call a sequence of constant-length morphisms torsion-free if any prime …

Modifying Besicovitch's construction of a set B of positive integers whose set of multiples MB
has no asymptotic density, we provide examples of such sets B for which η:= 1 Z\MB∈{0, 1} …

We investigate tameness of Toeplitz shifts. By introducing the notion of extended Bratteli-
Vershik diagrams, we show that such shifts with finite Toeplitz rank are tame if and only if …