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DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS Morris W. Hirsch University of California, Berkeley Stephen Smale University of California, Berkeley Robert L. Devaney Boston University
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DIFFERENTIAL EQUATIONS,
DY NA MI C A L SY ST EMS, A ND
AN INTRODUCTION
TO CHAOS

This is volume 60, 2ed in the PURE AND APPLIED MATHEMATICS Series
Founding Editors: Paul A. Smith and Samuel Eilenberg

DIFFERENTIAL EQUATIONS,
DY NA MICA L SY ST EMS, A ND
AN INTRODUCTION
TO CHAOS
Morris W. Hirsch
University of California, Berkeley
Stephen Smale
University of California, Berkeley
Robert L. Devaney
Boston University
Amsterdam Boston Heidelberg London New York Oxford
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Academic Press is an imprint of Elsevier

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This book is printed on acid-free paper.
Copyright 2004, Elsevier (USA)
All rights reserved.
No part of this publication may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopy, recording, or any information storage and
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Library of Congress Cataloging-in-Publication Data
Hirsch, Morris W., 1933-
Differential equations, dynamical systems, and an introduction to chaos/Morris W.
Hirsch, Stephen Smale, Robert L. Devaney.
p. cm.
Rev. ed. of: Differential equations, dynamical systems, and linear algebra/Morris W.
Hirsch and Stephen Smale. 1974.
Includes bibliographical references and index.
ISBN 0-12-349703-5 (alk. paper)
1. Differential equations. 2. Algebras, Linear. 3. Chaotic behavior in systems. I. Smale,
Stephen, 1930- II. Devaney, Robert L., 1948- III. Hirsch, Morris W., 1933-
Differential Equations, dynamical systems, and linear algebra. IV. Title.
QA372.H67 2003
515’.35--dc22
2003058255
PRINTED IN THE UNITED STATES OF AMERICA
030405060708987654321
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