One-Dimensional Dynamics
One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and comple
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Editorial Board E. Bombieri, Princeton S. Fefennan, Stanford M. Gromov, Bures-sur-Yvette H.W. Lenstra, Jr., Berkeley, P.-L. Lions, Paris R. Remmert (Managing Editor), Münster W. Schmid, Cambridge, Mass., J-P. Serre, Paris J.Tits, Paris
Welington de Melo Sebastian van Strien
One-Dimensional Dynamics With 89 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Welington de Melo Instituto deMatemätica Pura e Applicada Estrada Dona Castorina 110 22460 Rio de Janeiro, Brazil Sebastian van Strien Mathematics Department, University of Amsterdam Plantage Muidergracbt 24 1018 TV Amsterdam, Tbe Netberlands
MathematIcs Subject Classification (1991): 58Fxx, 34Cxx, 30-xx
ISBN-13:978-3-642-78045-5 e-ISBN-13:978-3-642-78043-1 001: 10.1007/978-3-642-78043-1 Library of Congress Cataloging-in-Publication Data Melo, Welington deo One-dimensional dynamies Welington de Melo, Sebastian van Strien. p. cm. (Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge, no. 25) Includes bibliographical references and index. ISBN-13: 978-3·{j42-78045-5 1. Differentiable dynamical systems. I.Strien, Sebastian van, 1956-. II. Title. III.Series. QA614.8.M45 1994 5l4'.74-dc20 93-7846 CIP Tbis work is subjcct to copyright. All rights are reserved, whetherthe whole or part of the material is concerned, spccifically thc 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 thercof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its currcnt 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 1993 Softcover reprint of the hardcover Ist edition 1993 Tbe 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. Typesetting: From dvi files by the authors 4113140 - 5432 I
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To Gilza, Hilary Daniel and David
Preface
One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the
