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.
- Book Title Substitution Dynamical Systems - Spectral Analysis
- Series Title Lecture Notes in Mathematics
- DOI https://doi.org/10.1007/978-3-642-11212-6
- Copyright Information Springer-Verlag Berlin Heidelberg 2010
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Softcover ISBN 978-3-642-11211-9
- eBook ISBN 978-3-642-11212-6
- Series ISSN 0075-8434
- Series E-ISSN 1617-9692
- Edition Number 2
- Number of Pages XV, 351
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Dynamical Systems and Ergodic Theory
Measure and Integration
- Buy this book on publisher's site
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)