56 citations · 231 across the 19 of their papers we have counts for
20 papers
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…
The carry propagation of the successor function
Valérie Berthé, Christiane Frougny, Michel Rigo +1
Given any numeration system, we call carry propagation at a number the number of digits that are changed when going from the representation of to the one of , and amor…
Balancedness and coboundaries in symbolic systems
Valérie Berthé, Paulina Cecchi Bernales
This paper studies balancedness for infinite words and subshifts, both for letters and factors. Balancedness is a measure of disorder that amounts to strong convergence properties…
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…
Brun expansions of stepped surfaces
Valérie Berthé, Thomas Fernique
Dual maps have been introduced as a generalization to higher dimensions of word substitutions and free group morphisms. In this paper, we study the action of these dual maps on par…
Specular sets
Valérie Berthé, Clelia De Felice, Vincent Delecroix +5
We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract general…
Return words of linear involutions and fundamental groups
Valérie Berthé, Vincent Delecroix, Francesco Dolce +3
We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincaré maps of measured foliations a suitable defin…
Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm
Valérie Berthé, Sébastien Labbé
The Arnoux-Rauzy-Poincaré multidimensional continued fraction algorithm is obtained by combining the Arnoux-Rauzy and Poincaré algorithms. It is a generalized Euclidean algorithm.…
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…
Critical connectedness of thin arithmetical discrete planes
Valérie Berthé, Damien Jamet, Timo Jolivet +1
An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its -connectedness. This…
Maximal bifix decoding
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurren…
Acyclic, connected and tree sets
Valerie Berthé, Clelia De Felice, Francesco Dolce +4
Given a set of words, one associates to each word in an undirected graph, called its extension graph, and which describes the possible extensions of on the left and…
Balance properties of Arnoux-Rauzy words
Valérie Berthé, Julien Cassaigne, Wolfgang Steiner
The paper deals with balances and imbalances in Arnoux-Rauzy words. We provide sufficient conditions for -balancedness, but our results indicate that even a characterization of…
Uniformly balanced words with linear complexity and prescribed letter frequencies
Valérie Berthé, Sébastien Labbé
We consider the following problem. Let us fix a finite alphabet A; for any given d-uple of letter frequencies, how to construct an infinite word u over the alphabet A satisfying th…
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…
Selfdual Substitutions in Dimension One
Valérie Berthé, Dirk Frettlöh, Victor Sirvent
There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselve…
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…
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…