Multidimensional Euclidean Algorithms, Numeration and Substitutions.
Valérie Berthé · 2011
The aim of this survey is to discuss multidimensional continued fraction and Euclidean algorithms from the viewpoint of numeration systems, substitutions, and the symbolic dynamical systems they generate. We will mainly focus on two types of multidimensional algorithms, namely, unimodular Markovian ones which include the most classical ones like e.g. Jacobi-Perron algorithm, and algorithms issued from lattice reduction. We will discuss these algorithms motivated by the study of substitutive dynamical systems, symbolic dynamical systems with low complexity function, and discrete geometry.