Singularity Theory and its Applications Warwick 1989, Part II: Singu
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geomet
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M. Roberts
1. Stewart (Eds.)
Singularity Theory and its Applications Warwick 1989, Part II: Singularties, Bifurcations and Dynamics
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Bareelona Budapest
Editors Mark Roberts Ian Stewart Mathematics Institute, University of Warwick Coventry CV4 7AL, United Kingdom
The figure on the front cover shows a genetic caustic in a 3-degree-of-freedom, timereversible Hamiltonian system, in a neighbourhood of a point of zero momentum. For details see the paper, Caustics in time-reversible Hamiltonian systems by J. Montaldi.
Mathematics Subject Classification (1980): 58C25, 58C27, 58C28, 58FlO, 58F14, 58F22, 58F27, 58F40
ISBN 3-540-53736-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-53736-8 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1991 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper
Preface A year-long symposium on Singularity Theory and its Applications was held at the University of Warwick in the academic year 1988-89. Two workshops were held during the Symposium, the first primarily geometrical and the second concentrating on the applications of Singularity Theory to the study of bifurcations and dynamics. Accordingly, we have produced two volumes of proceedings. One of the notable features of Singularity Theory is the close development of the theory and its applications, and we tried to keep this as part of the philosophy of the Symposium. liVe believe that we had some success. It should perhaps be pointed out that not all the papers included in these two volumes were presented at the workshops; these are not Proceedings of the workshops, but of the Symposium as a whole. In fact a considerable amount of the material contained in these pages was developed during the Symposium. For the record, the Symposium was organized by the four editors of the two volumes: David Mond, James Montaldi, Mark Roberts and Ian Stewart. There were over 100 visitors and 120 seminars. The Symposium was funded hy the S.E.R.C., and could not have been such a success without the hard work of Elaine Shiels, to whom we are all very grateful. Every paper published here is in final form and has been refereed.
Mark Roberts Ian Stewart University of 'Warwick, August 1990
Contents
P.J. Aston, Scaling laws and bifurcation
1
D.R.J. Chillingworth, Bifurcation from a manifold
22
P. Chossat & D
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