6 papers
On balance properties of hypercubic billiard words
Nicolas Bédaride, Valérie Berthé, Antoine Julien
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order…
Continuous eigenvalues of minimal subshifts via S-adic representations and coboundaries
Valérie Berthé, Paulina Cecchi-Bernales, Bastián Espinoza
We provide characterizations of continuous eigenvalues for minimal symbolic dynamical systems. These characterizations rely on a description of the system in terms of -adic stru…
Nonstationary Markov Partitions and Multidimensional Continued Fraction Algorithms
Pierre Arnoux, Valérie Berthé, Milton Minervino +2
It is well known from results of Sina\uı and Bowen that a hyperbolic toral automorphism admits a Markov partition. Our aim is to generalize this concept to the nonstationary case,…
Multidimensional statistics for finite orbits of generalised continued fractions
Valérie Berthé, Stephen Cantrell, Jungwon Lee +1
We statistically compare the relationships between frequencies of digits in continued fraction expansions of typical rational points in the unit interval and higher dimensional gen…
Automata on -adic words
Valérie Berthé, Toghrul Karimov, Mihir Vahanwala
A fundamental question in logic and verification is the following: for which unary predicates is the monadic second-order theory of $\langle \mathbb{N}; <, P_1,…
Density of rational languages under shift invariant measures
Valérie Berthé, Herman Goulet-Ouellet, Dominique Perrin
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied i…