North-Holland is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands c 2010 Elsevier B.V. All rights reserved Copyright No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email:
[email protected] Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13: 978-0-444-53141-4 For information on all North-Holland publications visit our web site at books.elsevier.com Printed and bound in USA 10 11 12 10 9 8 7 6 5 4 3 2 1 Preface The discipline of Nonlinear Dynamical Systems has expanded tremendously over the past five decades and the last couple of years several surveys and encyclopaedia have seen the light. The present book is the third volume of a Handbook that covers a wide range of subjects in the area. The chapters are written in such a way that the handbook forms an extensive entrance to the literature. The present volume focuses on the conceptual, and often geometric, aspects of the theory in the spirit of Poincar´e and Lyapunov and later of Andronov, Thom and Smale. Important notions of dynamical systems often are framed in terms of persistence under variation of initial positions and of system parameters. A particular case of this is that of structural stability under various equivalence relations like topological conjugacy or equivalence, amounting to the stable system being an interior point of its equivalence class. Often structural stability is a far too restrictive notion of persistence. A broader notion is provided by the idea of a generic property,