Let d≥ 1 be an integer and r=(r0,..., rd− 1)∈ Rd. The shift radix system τr: Zd→ Zd is defined
by τr (z)=(z1,..., zd− 1,−⌊ rz⌋) t (z=(z0,..., zd− 1) t). τr has the finiteness property if each z∈ …

Symbolic dynamics is essential in the study of dynamical systems of various types and is
connected to many other fields such as stochastic processes, ergodic theory, representation …

Our goal is to present a unified and reasonably complete account of the various conjectures,
known as Pisot conjectures, that assert that certain dynamical systems arising from …

Substitutions are combinatorial objects (one replaces a letter by a word) which produce
sequences by iteration. They occur in many mathematical fields, roughly as soon as a …

This paper studies geometric and spectral properties of S-adic shifts and their relation to
continued fraction algorithms. These shifts are symbolic dynamical systems obtained by …

We consider 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 recurrent tree …

Multidimensional continued fractions and symbolic codings of toral translations Page 1 ©
2022 European Mathematical Society Published by EMS Press and licensed under a CC BY …

A Sturmian sequence is an infinite nonperiodic string over two letters with minimal subword
complexity. In two papers, the first written by Morse and Hedlund in 1940 and the second by …

We study ternary sequences associated with a multidimensional continued fraction
algorithm introduced by the first author. The algorithm is defined by two matrices and we …

We define a generic algorithmic framework to prove a pure discrete spectrum for the
substitutive symbolic dynamical systems associated with some infinite families of Pisot …