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A combinatorial approach to products of Pisot substitutions
Tekijät: Berthe V, Bourdon J, Jolivet T, Siegel A
Kustantaja: CAMBRIDGE UNIV PRESS
Kustannuspaikka: bri
Julkaisuvuosi: 2016
Journal: Ergodic Theory and Dynamical Systems
Tietokannassa oleva lehden nimi: ERGODIC THEORY AND DYNAMICAL SYSTEMS
Lehden akronyymi: ERGOD THEOR DYN SYST
Vuosikerta: 36
Aloitussivu: 1757
Lopetussivu: 1794
Sivujen määrä: 38
ISSN: 0143-3857
DOI: https://doi.org/10.1017/etds.2014.141
Tiivistelmä
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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