Substitution Dynamical Systems - Spectral Analysis

Author:   Martine Queffélec
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2nd ed. 2010
Volume:   1294
ISBN:  

9783642112119


Pages:   351
Publication Date:   26 February 2010
Format:   Paperback
Availability:   Out of print, replaced by POD   Availability explained
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Substitution Dynamical Systems - Spectral Analysis


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Overview

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.

Full Product Details

Author:   Martine Queffélec
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2nd ed. 2010
Volume:   1294
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   1.160kg
ISBN:  

9783642112119


ISBN 10:   3642112110
Pages:   351
Publication Date:   26 February 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD   Availability explained
We will order this item for you from a manufatured on demand supplier.

Table of Contents

The Banach Algebra (T).- Spectral Theory of Unitary Operators.- Spectral Theory of Dynamical Systems.- Dynamical Systems Associated with Sequences.- Dynamical Systems Arising from Substitutions.- Eigenvalues of Substitution Dynamical Systems.- Matrices of Measures.- Matrix Riesz Products.- Bijective Automata.- Maximal Spectral Type of General Automata.- Spectral Multiplicity of General Automata.- Compact Automata.

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)


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)


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