Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems
An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurca
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Mariana Haragus r Gérard Iooss
Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems
Mariana Haragus Université de Franche-Comté Laboratoire de Mathématiques 25030 Besançon Cedex France [email protected]
Gérard Iooss IUF, Université de Nice Laboratoire J.A.Dieudonné 06108 Nice Cedex 02 France [email protected]
Editorial board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Universitá degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus Macintyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor Woyczynski, Case Western Reserve University
A co-publication with EDP Sciences, France, licensed for sale in all countries outside of France. Sold and distributed within France by EDP Sciences, 17, av. du Hoggar F-91944 Les Ulis, France EDP Sciences ISBN 978-2-7598-0009-4 ISBN 978-0-85729-111-0 e-ISBN 978-0-85729-112-7 DOI 10.1007/978-0-85729-112-7 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2010938140 Mathematics Subject Classification (2010): 34C20, 34C37, 34C45, 35B32, 35C07, 35Q35, 37G40, 37L10, 76B15, 76D05 © EDP Sciences 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of 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 laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is an extension of different lectures given by the authors during many years at the University of Nice, at the University of Stuttgart in 1990, and the University of Bordeaux in 2000 and 2001. Large parts of the first four chapters are of master level and contain various examples and exercises, partly posed at exams. However, the infinite-dimensional set-up in Chapter 2 requires several tools and results from the theory of linear o
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