Substitution dynamical systems. Spectral analysis
type: Item
instance of: scholarly article
title: Substitution dynamical systems. Spectral analysis
zbMATH Open document ID: 1225.11001
DOI: 10.1007/978-3-642-11212-6
author: Martine Queffélec
published in: Lecture Notes in Mathematics
publication date: 2010-04-27T00:00:00Z
review text: The first edition of this classical book appeared in 1987 [Substitution dynamical systems -- spectral analysis. Lecture Notes in Mathematics, 1294. Berlin etc.: Springer-Verlag (1987; Zbl 0642.28013)]. Since then, a large number of papers were devoted to automatic and substitutive (morphic) sequences including studies of associated dynamical systems and their spectral analysis. This new edition will make this book even more essential. The author intended to correct a few misprints but she was led to add chapters and to update the list of references. Chapters 1 to 12 correspond to the same chapters as in the first edition (addressing: Spectral theory of unitary operators and of dynamical systems, Dynamical Systems associated with sequences and arising from substitutions, Eigenvalues of substitutive dynamical systems, Matrices of measures, Matrix Riesz products, bijective automata, Maximal spectral type and spectral multiplicity of general automata, Compact automata). Two new chapters address respectively Schrödinger operators with substitutive potential, and substitutive continued fractions. The list of references contains about a hundred of items that have appeared since the first edition. All this makes this new edition a very important book that everybody interested in automatic and substitutive (morphic) sequences and their associated dynamical systems should definitely possess. Please note that some references are now available in journals: [32] \textit{E. Bombieri} and \textit{J. Bourgain}, J. Eur. Math. Soc. (JEMS) 11, No. 3, 627--703 (2009; Zbl 1170.42001); [65] \textit{M. J. Crabb}, \textit{J. Duncan} and \textit{C. M. McGregor}, Semigroup Forum 81, No. 1, 71--84 (2010; Zbl 1202.37014); [181] \textit{C. Mauduit} and \textit{J. Rivat}, Ann. Math. (2) 171, No. 3, 1591--1646 (2010; Zbl 1213.11025)].
reviewed by: Jean-Paul Allouche
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 28-02
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 5702308
zbMATH Keywords: substitution dynamical systems
zbMATH Keywords: automata sequences
zbMATH Keywords: morphic sequences
zbMATH Keywords: spectral analysis
zbMATH Keywords: Riesz products
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: ergodic theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-11212-6
OpenAlex ID: W4293517843
description: scientific article; zbMATH DE number 5702308