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Our first aim in this book is to explain the mathematical ideas The problems have beenĮxacerbated by the lack of suitable source material between theĮxtremes of hard-core topology and soft-centre popularization. They want qualities - though these sometimes acquire a fearsomelyĪlgebraic, even numerical, expression. Have numbers but, simply, most topologists don ' t want numbers, Tions, except that they asked themselves. Same goes for qualitatively with topologists and catastrophe descrip­ Ministically, replied that was how he was asked to design them. Thus Turing, charged that computers only operated deter­ Mathematicians to emphasize aspects of the theory that are notĪlways in sympathy with the practical requirements of the working Language in which the theory is couched, and the tendency of Standings may largely be traced to the unfamiliar mathematical Other fields where the problems are quite different. Riate mathematical formalism have been misinterpreted as definitiveĪpplications and disputes arising in these areas have contaminated To realms where its applicability is not guaranteed by the approp­ Shall account for in Chapter 7) has led some to infer that the theoryĬontains no new material at all. The theory in many fields (itself a product of the typicality that we 'purely qualitative', with a split between those who think this is a In some circles, too, the belief has arisen that catastrophe theory is Subject) have been repeated too often without proper qualification. Overstatements attributable to the 'youthful enthusiasm' for a new Tween elementary and non-elementary catastrophes, and partly Theory's universality (partly misstatements based on confusion be­ That in one context this requirement implied that the system couldīe described, locally, by one of seven standard forms, the elementaryĪs well as great interest, Thom's ideas have generated greatĬonfusion and, more recently, controversy. Stability, or insensitivity to small perturbations. Thom suggested using the topological theory ofĭynamical systems, originated by Poincare, to model discontinuousĬhanges in natural phenomena, with special emphasis on biology Īnd he pointed out the importance in this context of structural Has been a rapid growth of interest in the subject now known asĬatastrophe theory. Structurelle et Morphogenese, which finally appeared in 1972, there Since the first rumours in the mid- 1960's of Rene Thom's Stabilite Printed by photolithography and bound in Great Britain at The Pitman Otherwise without the prior written permission of the publishers.įilmset in Northern heland at The Universities Press (Belfast) Ltd. Means, electronic, mechanical, photocopying, recording and/or

Stored in a retrieval system, or transmitted in any form or by any No part of this publication may be reproduced, Pitman Publishing New Zealand Ltd, WellingtonĪMS Subject Classifications: (main) 58C25, 58E05Īll rights reserved. Passman, University of Wisconsin-MadisonĦ Davis Drive, Belmont, California 94002, USA Douglas, State University of New York at Stony Brook Jeffrey, University of Newcastle-upon-Tyne (Main Editor) SURVEYS AND REFERENCE WORKS IN MATH EMATICSĪ. Over 200 illustrations help clarify the ideas and applications in this volume, which will be of interest to researchers and postgraduate students in such diverse disciplines as engineering, mathematics, physics, and biology. The more controversial and speculative applications to areas in the social sciences are also mentioned, but not discussed in detail. Nearly half the book concentrates on detailed applications of the theory, emphasizing its uses in the physical sciences where applications can be made quantitative and can be experimentally verified. Thom's now-famous list of seven elementary catastrophes, broadly classifying various types of discontinuous change, is elucidated, as are the reasons for its appearance. The mathematical basis of the theory is therefore explained with a minimum of technicalities, although some knowledge of the calculus of variables is assumed. This first integrated treatment of the main ideas behind René Thom's theory of catastrophes aims to make them accessible to scientists wishing to apply the theory in their own fields of research.