Auteur / Autrice : | Bo Tan |
Direction : | Jacques Peyrière, Zhi-Xiong Wen |
Type : | Thèse de doctorat |
Discipline(s) : | Mathématiques |
Date : | Soutenance en 2002 |
Etablissement(s) : | Paris 11 en cotutelle avec Université de Wuhan (Chine) |
Partenaire(s) de recherche : | autre partenaire : Université de Paris-Sud. Faculté des sciences d'Orsay (Essonne) - Université de Wuhan. Nonlinear Science Center (Chine) |
Mots clés
Résumé
This work deals with sequences of low complexity. Their properties are studied from different viewpoints: combinatorial, arithmetic, and geometric. The four first chapters are devoted to study the following properties of sequences over a two-letter alphabet: factors composition matrix, geometric generation of sturmian sequences, local isomorphism, and characterization of substitutions having two fixed points which differ only by a prefix. In the following two chapters, substitutions on a three-letter alphabet are studied. In chapter 7, it is shown that the spectrum of a discrete Schrodinger operator whose potential is generated by a primitive and non-periodic substitution has zero Lebesgue measure. The last chapter deals with topological properties of attractors of IFSs.