Substitutions in Dynamics, Arithmetics and Combinatorics

Lecture Notes in Mathematics

N. Pytheas Fogg

420 pages, parution le 18/11/2002

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Résumé

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the '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 of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Contents

Basic notions on substitutions

Part I: Arithmetics and combinatorics of substitutions

Substitutions, arithmetic and finite automata: an introduction
Automatic sequences and transcendence
Substitutions and partitions of the set of positive integers

Part II: Dynamics of Substitutions

Substitutions and symbolic dynamical systems
Sturmian Sequences
Spectral theory and geometric representation of substitutions
Diophantine approximations, substitutions, and fractals

Part III: Extensions to free groups and interval transformations

Infinite words generated by invertible substitutions
Polynomial dynamical systems associated with substitutions
Piecewise linear transformations of the unit interval and Cantor sets
Some open problems

A. Undecomposable matrices in dimension 3

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	N. Pytheas Fogg
Parution	18/11/2002
Nb. de pages	420
Format	15,5 x 23,5
Couverture	Broché
Poids	630g
Intérieur	Noir et Blanc
EAN13	9783540441410