文档介绍：Perspectives of nonlinear dynamics
To my lieveling, Cindi, and
our wonderful sons, Eric and Mark.
This study is dedicated to their
growing appreciation of the wonders
and beauties in life
VOLUME 1
Perspectives of nonlinear
dynamics
E. ATLEE JACKSON
AMBRIDGE
UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: 0521345040
© Cambridge University Press 1989
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 1989
First paperback edition (with corrections) 1991
Reprinted 1995
Re-issued in this digitally printed version 2008
A catalogue record for this publication is available from the British Library
ISBN 978-0-521-34504-0 hardback
ISBN 978-0-521-42632-9 paperback
Contents of Volume 1
Preface ix
Acknowledgements xii
Concepts related to nonlinear dynamics: historical outline xiii
1 In the beginning... 1
...there was Poincare 1
What are `nonlinear phenomena'?; projections, models, and some relationships
between linear and nonlinear differential equation 3
Two myths: a linear and analytic myth 8
Remarks on modeling: pure mathematics vis a vis `empirical' mathematics 10
The ordering anization of ideas: dynamic dimensions, continuous and
discrete variables; the analytic, qualitative, computational, and experimental
approaches to nonlinear dynamics; Sneaking up on plexity of dynamics 12
Some thoughts: Albert Einstein, Victor Hugo, . Pippard, Richard Feynman,
Henri Poincare 15
Comments on exercises 16
2 A potpourri of basic conc