56 citations · 231 across the 19 of their papers we have counts for
5 papers · 1 filter
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…
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…
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.…
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…