Substitution Dynamical Systems - Spectral Analysis: 1294 (Lecture Notes in Mathematics, 1294) - Softcover

Queffélec, Martine

Softcover

ISBN 10: 3642112110 ISBN 13: 9783642112119

Publisher: Springer, 2010

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2010
• Language: English
• ISBN 10: 3642112110
• ISBN 13: 9783642112119
• Binding: Paperback
• Edition number: 2
• Number of pages: 366