Lecture Notes in Mathematics

Substitution Dynamical Systems - Spectral Analysis

Authors: Queffélec, Martine

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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.

Reviews

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)


Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-11212-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.95
price for USA
  • ISBN 978-3-642-11211-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Substitution Dynamical Systems - Spectral Analysis
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1294
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-11212-6
DOI
10.1007/978-3-642-11212-6
Softcover ISBN
978-3-642-11211-9
Series ISSN
0075-8434
Edition Number
2
Number of Pages
XV, 351
Topics