Sur l'ensemble normal des substitutions de longueur quelconque. (On the normal set of substitutions of arbitrary length)
type: Item
instance of: scholarly article
title: Sur l'ensemble normal des substitutions de longueur quelconque. (On the normal set of substitutions of arbitrary length)
zbMATH Open document ID: 0655.10053
DOI: 10.1016/0022-314X(88)90103-5
author: Christian Mauduit
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Let the sequence \(u=(u_ n)\) of integers be a fixed point under a substitution of arbitrary length. Let B(u) denote the normal set associated with u, i.e. the set of all real numbers x such that \((u_ nx)\) is uniformly distributed modulo 1. It is proved that \({\mathbb{R}}\setminus B(u)\) is contained in a finite extension of the rationals if u is not too ``lacunary''. Thus earlier results of \textit{J. Coquet} [J. Number Theory 16, 363-375 (1983; Zbl 0512.10041)] on automatic sequences are generalized.
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 11K06
zbMATH DE Number: 4069013
zbMATH Keywords: normal number
zbMATH Keywords: uniform distribution
zbMATH Keywords: substitution
reviewed by: Robert F. Tichy
MaRDI profile type: Publication
cites work: Q4096964
cites work: Suites algébriques, automates et substitutions
cites work: Uniform tag sequences
cites work: Graphes connexes représentation des entiers et équirepartition
cites work: Mixing properties of substitutions
cites work: Minimal flows arising from substitutions of non-constant length
cites work: Automates finis et ensembles normaux. (Finite automata and normal sets)
cites work: Morphismes unispectraux. (Unispectral morphisms)
cites work: Q4103613
cites work: Nombres algébriques et substitutions
cites work: Q4140407
cites work: Q5332701
cites work: Q5342712
Recommended article: Caractérisation des ensembles normaux substitutifs. (Characterization of normal substitutional sets)
Recommended article: Remarques sur la suite engendrée par des substitutions composées
Recommended article: Q3497155
Recommended article: Q3333139
Recommended article: Sur la transitivité et la primitivité des groupes de substitutions
description: scientific article; zbMATH DE number 4069013