Dynamical Systems and Bifurcations Proceedings of a Workshop held in
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1125 Dynamical Systems and Bifurcations Proceedings of a Workshop held in Groningen The Netherlands, April 16-20, 1984
Edited by B. L. J. Braaksma, H. W Broer and F. Takens
Springer-Verlag Berlin Heidelberg New York Tokyo
Editors
Boele L. J. Braaksma Hendrik W. Broer Floris Takens Rijksuniversiteit Groningen, Subfaculteit Wiskunde en Informatica Landleven 5, 9747 AD Groningen, The Netherlands
Mathematics Subject Classification (1980): 58-xx, 34Cxx ISBN 3-540-15233-4 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-15233-4Springer-Verlag New York Heidelberg Berlin Tokyo 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 "Vervvertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
PREFACE
These are the proceedings of the International Workshop on Dynamical Systems and Bifurcations, organized by the Department of Mathematics of Groningen University from April 16 to April 20, 1984. Apart from Groningen University financial support was given by various instances: Koninklijke Shell B.V., de Koninklijke Nederlandse Akademie van Wetenschappen and the Netherlands Organization for the Advancement of Pure Research (ZWO). The informal atmosphere among the participants of the Workshop made it possible that there was an intensive exchange of mathematical ideas. We are grateful to all who contributed to the success of our Workshop, in particular to the lecturers and to the authors of these proceedings.
B.L.J.B., H. W.B., F.T. Groningen, march 1985.
TAB LEO F
CON TEN T S
M. Chaperon An elementary proof of the Conley-Zehnder theorem in symplecti c geometry ••••••.. R. Dieckerhoff and E. Zehnder An "a priori" estimate for oscillatory equations.................................
9
F. Dumortier On the structure of germs of vector fields in R3 whose linear part generates rotations.............................................................
15
A. Floer and E. Zehnder Fixed point results for symplectic maps related to the Arnold-conjecture .•••••..
47
J. Palis and R. Roussarie Topological invariants as numbers of translations ••••.••..••....•.......••••.••.
64
J.A. Sanders and R. Cushman Abelian integrals and global Hopf bifurcations ..••..•••.••••••.........••.•.•... 87 F. Takens On the numerical determination of the dimension of an attractor ...•...•••.••..•.
99
G. Vegter Global stability of generic two-parameter families of gradients on three-manifolds •••......•...•••••..•....••......•..••.•••..•.••.........•••.••••. 107
AN ELEMENTARY PROOF OF THE CONLEY - ZEHNDER THEOREM IN SYMPLECTIC GEOMETRY. Marc CHAPERON Centre de Mathematiques Ecole Polyte
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