Substitution Dynamical Systems - Spectral Analysis
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
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1294
Martine Queffélec
Substitution Dynamical Systems – Spectral Analysis Second Edition
123
Martine Queffélec Université Lille 1 Laboratoire Paul Painlevé 59655 Villeneuve d’Ascq CX France [email protected]
ISBN: 978-3-642-11211-9 e-ISBN: 978-3-642-11212-6 DOI: 10.1007/978-3-642-11212-6 Springer Heidelberg Dordrecht London NewYork Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2010920970 Mathematics Subject Classification (2000): 37, 42, 11, 28, 47, 43, 46, 82 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: SPi Publisher Services Printed on acid-free paper springer.com
Preface for the Second Edition
This revised edition initially intended to correct the misprints of the first one. But why does it happen now, while the subject extensively expanded in the past twenty years, and after the publication of two major books (among other ones) devoted to dynamical systems [88] and automatic sequences [14]? Let us try to explain why we got convinced to do this new version. On the one hand, the initial account of the LNM 1294 offered a basis on which much has been built and, for this reason, it is often referred to as a first step. On the other hand, the two previously quoted books consist in impressive and complete compilations on the subject [14, 88]; this was not the spirit of our LNM, almost self-contained and “converging” to the proof of a specific result in spectral theory of dynamical systems. From this point of view, those three books might appear as complementary ones. This having been said, reproducing the corrected LNM identically would have been unsatisfactory : a lot of contributions have concurred to clarify certain aspects of the subject and to fix notations and definitions; also a great part of the raised questions have now been solved. Mentioning these improvements seemed to us quite necessary. Therefore, we chose to add some material to the first introductory chapters, which of course does not (cannot) reflect the whole progress in the field but some interesting directions. Moreover, two applications of substitutions more generally of combinatorics of words - to
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