43 citations · 44 across the 4 of their papers we have counts for
4 papers
Meyer sets, Pisot numbers, and self-similarity in symbolic dynamical systems
Valérie Berthé, Reem Yassawi
Aperiodic order refers to the mathematical formalisation of quasicrystals. Substitutions and cut and project sets are among their main actors; they also play a key role in the stud…
Density of group languages in shift spaces
Valérie Berthé, Herman Goulet-Ouellet, Carl-Fredrik Nyberg-Brodda +2
The density of a rational language can be understood as the frequency of some pattern in the shift space, for example a pattern like "words with an even number of a given letter."…
The Monadic Theory of Toric Words
Valérie Berthé, Toghrul Karimov, Joël Ouaknine +2
For which unary predicates is the MSO theory of the structure decidable? We survey the state of the art, leadin…
Geometry, dynamics, and arithmetic of -adic shifts
Valérie Berthé, Wolfgang Steiner, Jörg Thuswaldner
This paper studies geometric and spectral properties of -adic shifts and their relation to continued fraction algorithms. These shifts are symbolic dynamical systems obtained by…