Titlebook: Substitutions in Dynamics, Arithmetics and Combinatorics; N. Pytheas Fogg,Valéré Berthé,Anne Siegel Book 2002 Springer-Verlag Berlin Heide

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Automatic sequences and transcendenceeal case, it is well known that the expansion in a given integer basis of a rational number is ultimately periodic, which implies that its complexity function is bounded. More generally, the expansion of an algebraic irrational number in a given integer basis is supposed to be normal, whereas real n

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Substitutions and symbolic dynamical systemsTo improve lisibility, some of the definitions and propositions stated in Chap. 1 are repeated in the present chapter..In the course of this chapter, we shall use at some points notions of measure theory and spectral theory; when there is no explanation in the text, the reader is referred to any sta

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Sturmian Sequencesonally independent periods; this is a very typical situation, arising for example in astronomy (with the rotation of the moon around the earth, and of the earth around the sun), or in music (with the building of musical scales, related to the properties of log 3/log 2), and such sequences have been

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Diophantine approximations, substitutions, and fractalse Rauzy fractal [350] (see also Chap. 7). The substitutions are of Pisot type and unimodular, and our method is constructive. In this way, we obtain a geometric representation of the substitution as a domain exchange and, with a stronger hypothesis, we get a rotation on a torus. In fact, there are t

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0075-8434 ‘simplest‘ possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure..The authors describe the concepts of quantity

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