© 2010

Substitution Dynamical Systems - Spectral Analysis


Part of the Lecture Notes in Mathematics book series (LNM, volume 1294)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Martine Queffélec
    Pages 1-19
  3. Martine Queffélec
    Pages 21-48
  4. Martine Queffélec
    Pages 49-86
  5. Martine Queffélec
    Pages 87-124
  6. Martine Queffélec
    Pages 125-160
  7. Martine Queffélec
    Pages 161-192
  8. Martine Queffélec
    Pages 193-207
  9. Martine Queffélec
    Pages 209-224
  10. Martine Queffélec
    Pages 225-242
  11. Martine Queffélec
    Pages 243-264
  12. Martine Queffélec
    Pages 265-280
  13. Martine Queffélec
    Pages 281-291
  14. Back Matter
    Pages 293-351

About this book


This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains.
As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters.
This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples.
Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.


Banach algebra Eigenvalue Maximum calculus dynamical system ergodic theorem maximal spectral type spectral multiplicity substitution

Authors and affiliations

  1. 1.Technologies de LilleUniversité des Sciences etVilleneuve d'Ascq CXFrance

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From the reviews of the second edition:

“The first edition of this classical book appeared in Substitution dynamical systems – spectral analysis, Lecture Notes in Mathematics … . a very important book that everybody interested in automatic and substitutive (morphic) sequences and their associated dynamical systems should definitely possess.” (Jean-Paul Allouche, Zentralblatt MATH, Vol. 1225, 2012)