Sur l'ensemble normal des substitutions de longueur quelconque. (On the normal set of substitutions of arbitrary length)
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.
scientific article; zbMATH DE number 4069013
scientific article