Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functi
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Robert Roussarie
Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
Modern Birkhäuser Classics Many of the original research and survey monographs in pure and applied mathematics, as well as textbooks, published by Birkhäuser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers.
Robert Roussarie
Bifurcations of Planar Vector Fields and Hilbert’s Sixteenth Problem
Reprint of the 1998 Edition
Robert Roussarie Institut de Mathématique Université de Bourgogne Dijon, France
ISBN 978-3-0348-0717-3 ISBN 978-3-0348-0718-0 (eBook) DOI 10.1007/978-3-0348-0718-0 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2013953592 Mathematics Subject Classification (2010): 58-XX, 34C05, 34C23, 35B32, 37G15, 37G99, 37-02 © Springer Basel 1998 Reprint of the 1st edition 1998 by Birkhäuser Verlag, Switzerland Originally published as volume 164 in the Progress in Mathematics series This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover design: deblik, Berlin Printed on acid-free paper Springer Basel is part of Springer Science+Bus
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