53 citations · 65 across the 11 of their papers we have counts for
14 papers
Rational approximations, multidimensional continued fractions and lattice reduction
Valerie Berthé, Karma Dajani, Charlene Kalle +3
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps…
On the rigidity of Arnoux-Rauzy words
Valérie Berthé, Svetlana Puzynina
An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of a same substitution. Sturmian words as well as characteristic Arnou…
A note on one-sided recognizable morphisms
Marie-Pierre Béal, Valérie Berthé, Dominique Perrin +1
We revisit the notion of one-sided recognizability of morphisms and its relation to two-sided recognizability.
Lochs-type theorems beyond positive entropy
Valérie Berthé, Eda Cesaratto, Pablo Rotondo +1
Lochs' theorem and its generalizations are conversion theorems that relate the number of digits determined in one expansion of a real number as a function of the number of digits g…
Coboundaries and eigenvalues of finitary S-adic systems
Valérie Berthé, Paulina Cecchi Bernales, Reem Yassawi
An S-adic system is a symbolic dynamical system generated by iterating an infinite sequence of substitutions or morphisms, called a directive sequence. A finitary S-adic dynamical…
Dynamics of Ostrowski skew-product: I. Limit laws and Hausdorff dimensions
Valérie Berthé, Jungwon Lee
We present a dynamical and spectral study of Ostrowski's map based on the use of transfer operators. The Ostroswki dynamical system is obtained as a skew-product of the Gauss map (…