Substitutions in Dynamics, Arithmetics and Combinatorics
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a wo
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N. Pytheas Fogg
Substitutions in Dynamics, Arithmetics and Combinatorics Editors: V. Berthé S. Ferenczi C. Mauduit A. Siegel
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Author N. Pytheas Fogg Marseille, France
Editors Valérie Berthé Sébastien Ferenczi Christian Mauduit Univ. de la Méditerranée IML, Case 907 163 av. de Luminy 13288 Marseille Cedex 09, France e-mail: [email protected] [email protected] [email protected]
Anne Siegel IRISA Campus de Beaulieu 35042 Rennes Cedex France e-mail: [email protected]
Authors’ name: N. stands for "no nomen". Pytheas was the Greek navigator and scientist (4th century B.C.) who became one of the historical heroes of the city of Marseille (Massalia). Phileas Fogg was the excentric and phlegmatic hero of Jules Verne who travelled around the world by "jumbing mathematically from train to boat, never forgetting his sense of humour."
Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek - CIP-Einheitsaufnahme Pytheas Fogg, N.: Substitutions in dynamics, arithmetics and combinatorics / N. Pytheas Fogg. Ed.: V. Berthé .... - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in mathematics ; 1794) ISBN 3-540-44141-7
Mathematics Subject Classification (2000): 11B85, 1A55, 11a63, 11j70, 11kxx, 11ro6, 28a80, 28dxx, 37axx, 37bxx, 40a15, 68q45, 68r15 ISSN 0075-8434 ISBN 3-540-44141-7 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm 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-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the editors SPIN: 10890994
41/3142/du - 543210 - Printed on acid-free paper
Preface
There are two basic ways of constructing dynamical systems. One approach is to take an already existing system from the vast reserve arising in biology, physics, geometry, or probability; such systems are typically rather complex and equipped with rigid structures (a “natural” system is generally a “smooth” system). Alternatively one can build a system by hand u
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