Proceedings of the Symposium on Differential Equations and Dynamical Systems
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206 Proceedings of the Symposium on Differential Equations and Dynamical Systems University of Warwick September 1968 - August 1969 Summer School, July 15 - 25, 1969
Edited by David Chillingworth, University of Warwick, Coventry, Warwickshire/G.B.
Springer-Verlag Berlin· Heidelberg· NewYork 1971
AMS Subject Classifications (1970): 34-02, 58-02, 57D 30
ISBN 3-540-05495-2 Springer-Verlag Berlin' Heidelberg· New York ISBN 0-387-05495-2 Springer-Verlag New York· Heidelberg· Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin' Heidelberg 1971. Library of Congress Catalog Card Number 79-164%1. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbach
INTRODUCTION These notes were taken from seminars and lectures given ln the Mathematics Institute of the University of Warwick during the Symposium on Differential Equations and Dynamical Systems held between 1 st September 19 6 8 and 31 st August 19 6 9, and from lectures given in the Arts Lecture Theatre of the University during the Summer School in July 1969. The organization of the Symposium and the Summer School would not have been possible without the generous support of the Science Research Council, to whom we are extremely grateful.
The
focus for the Symposium was the Mathematics Research Centre, which is partially supported by the Nuffield Foundation, to whom we are also very grateful. L.
We extend our particular thanks to Professor
Markus, the Nuffield Professor, for his energies in running the
Symposium so successfully. The notes are presented in approximately chronological order, with the exception of the Summer School lectures which are placed at the end and the talks from a sub-seminar on Foliations which are collected together.
Some of the lectures were expositions of work
already published, while others announced results which were obtained during the course of the Symposium.
The level of familiar-
ity of the audience with the subject matter which was assumed by the speakers varied considerably, and so terms left undefined in one lecture may frequently be found explained in another.
To avoid
repetition, some standard notation which is used throughout (except where stated otherwise) is collected on page XI.
References
[1]
indicate the references at the end of each lecture, and references
(£) refer to other lectures in these Proceedings.
Many of the
references given as "to appear" have now appeared; in particular,
IV the Proceedings of the A.M.S. Summer Institute on Global Analysis, Berkeley, 1968 Bre now in print.
A good general background to many
of the topics and their motivati
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