A1 Refereed original research article in a scientific journal
A combinatorial approach to products of Pisot substitutions
Authors: Berthe V, Bourdon J, Jolivet T, Siegel A
Publisher: CAMBRIDGE UNIV PRESS
Publishing place: bri
Publication year: 2016
Journal: Ergodic Theory and Dynamical Systems
Journal name in source: ERGODIC THEORY AND DYNAMICAL SYSTEMS
Journal acronym: ERGOD THEOR DYN SYST
Volume: 36
First page : 1757
Last page: 1794
Number of pages: 38
ISSN: 0143-3857
DOI: https://doi.org/10.1017/etds.2014.141
Abstract
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 substitutions. We focus on the families obtained as finite products of the three-letter substitutions associated with the multidimensional continued fraction algorithms of Brun and Jacobi-Perron. Our tools consist in a reformulation of some combinatorial criteria (coincidence conditions), in terms of properties of discrete plane generation using multidimensional (dual) substitutions. We also deduce some topological and dynamical properties of the Rauzy fractals, of the underlying symbolic dynamical systems, as well as some number-theoretical properties of the associated Pisot numbers.
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 substitutions. We focus on the families obtained as finite products of the three-letter substitutions associated with the multidimensional continued fraction algorithms of Brun and Jacobi-Perron. Our tools consist in a reformulation of some combinatorial criteria (coincidence conditions), in terms of properties of discrete plane generation using multidimensional (dual) substitutions. We also deduce some topological and dynamical properties of the Rauzy fractals, of the underlying symbolic dynamical systems, as well as some number-theoretical properties of the associated Pisot numbers.
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