Substitutions in Dynamics, Arithmetics and Combinatorics

Preface

1. Basic notions on substitutions
Valérie Berthé and Anne Siegel
Chapter 1

PartI Arithmetics and Combinatorics of substitutions

2. Substitutions, arithmetic and finite automata: an introduction
Christian Mauduit
Chapter 2

3. Automatic sequences and transcendence
Valérie Berthé
Chapter 3

4. Substitutions and partitions of the set of positive integers
Jun-Ichi Tamura
Chapter 4

PartII Dynamics of substitutions

5. Substitutions and symbolic dynamical systems
Sébastien Ferenczi
Chapter 5

6. Sturmian sequences
Pierre Arnoux
Chapter 6

7. Spectral theory and geometric representation of substitutions
Anne Siegel
Chapter 7

8. Diophantine approximations, substitutions, and fractals
Shunji Ito
Chapter 8

PartIII Extensions to free groups and interval transformations

9. Infinite words generated by invertible substitutions
Zhi-Ying Wen
Chapter 9

10. Polynomial dynamical systems associated with substitutions
Jacques Peyrière
Chapter 10

11. Piecewise linear transformationq of the unit interval and Cantor sets
Makoto Mori
Chapter 11

11. Some open problems
Valérie Berthé and Pierre Arnoux
Chapter 12

A. Undecomposbale matrices in dimension 3
Joel Rivat
Appendix

References and index
Bibliography

Index
Index