26 citations · 73 across the 7 of their papers we have counts for
7 papers
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…
Connectedness of fractals associated with Arnoux-Rauzy substitutions
Valérie Berthé, Timo Jolivet, Anne Siegel
Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limi…
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…
Rational numbers with purely periodic -expansion
Boris Adamczewski, Christiane Frougny, Anne Siegel +1
We study real numbers with the curious property that the -expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real number…
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…