56 citations · 231 across the 19 of their papers we have counts for
7 papers · 1 filter
On The Dimension Group of Unimodular S-Adic Subshifts
Valerie Berthe, P Cecchi Bernales, Fabien Durand +3
Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely gen…
Recognizability for sequences of morphisms
Valérie Berthé, Wolfgang Steiner, Jörg Thuswaldner +1
We investigate different notions of recognizability for a free monoid morphism . Full recognizability occurs when each (aperiodic) point in $\ma…
A combinatorial approach to products of Pisot substitutions
Valérie Berthé, Jérémie Bourdon, Timo Jolivet +1
We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substituti…
Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
Valérie Berthé, Timo Jolivet, Anne Siegel
We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explic…
Fractal tiles associated with shift radix systems
Valérie Berthé, Anne Siegel, Wolfgang Steiner +2
Shift radix systems form a collection of dynamical systems depending on a parameter which varies in the -dimensional real vector space. They generalize well-known n…
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions
S. Akiyama, G. Barat, V. Berthe +1
This paper studies tilings related to the beta-transformation when beta is a Pisot number (that is not supposed to be a unit). Then it applies the obtained results to study the set…
Purely periodic beta-expansions in the Pisot non-unit case
Valerie Berthe, Anne Siegel
It is well known that real numbers with a purely periodic decimal expansion are the rationals having, when reduced, a denominator coprime with 10. The aim of this paper is to exten…