Functional Differential Equations and Approximation of Fixed Points: Proceedings, Bonn, July 1978

509 Pages·1979·6.11 MB·English

by  J. C. Alexander (auth.)

Lecture Notes ni
Mathematics
Edited by A. Dold and B. Eckmann
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:resivdA .F hcurbezriH
730
Functional Differential Equations
and
Approximation of Fixed Points
Proceedings, Bonn, July 1978
Edited by
Heinz-Otto Peitgen and Hans-Otto Walther
galreV-regnirpS
nilreB grebledieH weN kroY 91 9 7
Editors
Heinz-Otto Peitgen
Fachbereich Mathematik
Universit~t Bremen
D-2800 Bremen 33 / FRG
Hans-Otto Walther
Mathematisches Institut
ti~tisrevinU MLinchen
D-8000 MLinchen 2 / FRG
AMS Subject Classifications (1970): 34JXX, 34 KXX, 65 D15, 65L15
ISBN 3-540-09518-7 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-09518-7 Springer-Verlag New York Heidelberg Berlin
Library of Congress Cataloging m Publication Data
Summerschool and Conference on Functional Differential Equations and Approximation
of Fixed Points, University of Bonn. 1978.
Functional differential equations and approxtmation of fixed points.
(Lecture notes in mathematics ; 730)
Bibhograhy: .p
Includes index.
.1 Functional differential equations--Congresses. 2. Fixed point thc'ory--Congr(.'sses.
3. Approximation theory--Congresses. .I Peitgen, Heinz-Otto, 1945-
.1I Walther, Hans-Otto: Ill. Title. .VI Series:
Lecture notes in mathematics (Berlin) ; 730.
QA3.L28 no. 730 QA372 510'.8s 515'.35
ISBN 0-387-09518-7
79-16224
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,
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similar means, and storage in data banks. Under 96 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
t.(( by Springer-Verlag Berlin Heidelberg 1979
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2141/3140-543210
~re~,~,2ii~ed to Heinz re~9~.L
.ro occasion, o~ ~ his
~3( h~! birvh~ay
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PREFACE
This volume comprises the proceedings of the Summerschool and Conference on
Functional Differential Equations and Approximation of Fixed Points held at the
University of Bonn, July 71 - 22, 1978. The conference was sponsored by
Sonderforschungsbereich ,27 Deutsche Forschungsgemeinsahaft, at the Institut
f~r Angewandte Mathematik der Universit~t Bonn.
Morning sessions were occupied by comprehensive survey talks given by
.J .C Alexander University of Maryland
.B .C Eaves Stanford University
.J .K Hate Brown University
.J Mallet-Paret Brown University
.R .D Nussbaum Rutgers University
.R Saigal Northwestern University
In the afternoon there were seminar meetings and invited addresses about
recent progress in the two fields. Seminars covering informal discussions and re-
search announcements were conducted by .E Allgower, .B .C Eaves, .J .K Hale,
and .R .D Nussbaum.
The motivation to bring together the two topics in one conference was twofold:
First, our group .N( Angelstorf, K. Georg, H. Peters, M. Prfifer, H. W. Siegberg
and myself) had made some progress and was interested (cf. publications in these
IV
proceedings) in understanding functional differential equations using simplicial
fixed point algorithms . Moreover, we elt that it might be of interest for
younger colleagues in this country to find ~n introduction into these mushrooming
fields of current research in numerical and nonlinear analysis. nI view of this
it was a great pleasure to welcome in the meeting more than 140 participants from
61 different countries.
1978 has been the 50 th anniversary of Sperner's Lemma which was certainly at
the heart of many of the results presented. The conference was delighted to have
.'E ,~enr~:r~ as a participant and lecturer.
I wish to express my thanks to the lecturers, to all participants who supported
the meeting, to the authors having forwarded their papers and to all those who
refereed for this volume.
A particular measure of gratitudc si due to .'i AJf.9"o!~' for his advice during
the early planning of the meeting, to .T ,F.'I~,v'~f~.'~A .fi ,s,ze;'.d;i, .U. ,:!~f.;!r~i ,,' and
.H .'~i 9,x~.bSe~ff - for their indispensable assistance in the preparation and con-
duction of the conference and this volume, to .:: .? ~'/aT~,~P for his careful co-
operation in editing these proccedinF, s , to b4. n.:;oJ'l~:~,~J.~'.~. who as chairman of
Sonderforschungsbereich 72 encouraged us to keep on with the idea and format of the
meeting, and finally to Mrs. ~i~ .cif'..J~v~2? , for her invaluable help and patience in
al secretarial and administrative matters.
February 1979 lleinz-Otto Peitgen
Un~versit~t Bremen and
Sonderforschungsbereich 72,
Univers~t~t Bonn
+%
The symbol of the conference was designed to express a link between the two
topics: it shows simplicia approximation techniques in the study of global bi-
furcation for functional differential equations.
PARTICIPANTS
D. ABTS Aachen C. FENSKE GieBen
J.C. ALEXANDER College Park .B FIEDLER Heidelberg
E. ALLGOWER Fort Collins P.M. FITZPATRICK College Park
W. ALT Heidelberg D. FLOCKERZI WHrzburg
H. ~MANN Kiel W. FORSTER Southampton
J. ANDRES Bonn G. FOURNIER Sherbrooke
N. ANGELSTORF Bonn .S FRYDRYCHOWICZ Berlin
J. APPELL Berlin M. FUR1 Florenz
0. ARINO Pau J. G~IST Bremen
.B AULBACH WHrzburg K. GEORG Bonn
L. B%CKSTROM V~xj8 K.P. HADELER Tibingen
H.T. BANKS Providence J.K. KALE Providence
F.S. DE BLASI FLorenz G. v.HARTEN Paderborn
R. BORELLI Bonn .S HEIMSATH Bremen
.B BROSOWSKI Bonn U. EKI~LEH Bremen
.H BULEY Aachen G. HETZER Aachen
J. CANAVATI Mexico D. HINRICHSEN Bremen
S.N. CHOW East Lansing W. HOFMANN Hamburg
F. COLONIUS Bremen T. IIORION Aachen
.G COOPERMAN Providence V.J. ISTRATESCU Frankfurt
L. CKO~E GSttingen J. IZE Mexico
N. DANCER Armidale W. J~GER Heidelberg
J. DANE S Prag H. JEGGLE Berlin
K. DEIMLING Paderborn H. JURGENS Bremen
D. DENNEBERG Bremen J.L. KAPLAN Boston
W. DESCH Graz F. KAPPEL Graz
M.L. DIVlCCARO Neapel .S KASPAR Graz
E.L. DOZO BrHssel R.B. KELLOGG College Park
.B DUPUIS Louvain-la-Neuve J.S. KIM Seoul
.J DYSON Oxford K. KIRCHGASSNER Stuttgart
B.C. EAVES Stanford U. KIRCHGRABER ZHrich
.H ENGL Linz D. KRONER Aachen
G. EISEN Bonn K. KUNISCH Graz
H. ENGLER Heidelberg G. v.d. LAAN Amsterdam
C. FABRY Louvain-la-Neuve J.M. LASRY Paris
IIIV
A. LETTIERI Neapel E. SPERNER Sulzburg-Laufen
T.Y. LI East Lansing K.W. SCHAAF Heidelberg
.S LUCKHAUS Heidelberg R. SCHAAF Heidelberg
W. MACKENS Bochum .B SCHAFFRIN Bonn
J. MALLET-PARET Providence W. SCHAPPACHER Graz
E. MALUTA Mailand K. SCHERER Bonn
G. MANCINI Bologna J. SCHEURLE Stuttgart
.S MASSA Mailand D. SCHMIDT mssen
W. MANTHEY Bremen A. SCHMIEDER Bremen
N. MATZL Graz K. SCHMITT Salt Lake City
H. MAURER MHnster E. SCHOCK Kaiserslautern
K. MERTEN Bremen K. SCHUMACHER THbingen
H. MONCH Paderborn R. SCHONEBERG Aachen
G. MULLER Aachen C. SCHUPP MHnchen
H.F. MONZNER Bremen J. SPREKELS Hamburg
J.A. ,TEHON Madison U. STAUDE Mainz
R.D. NUSSBAUM New Brunswick H. STEINLEIN MHnchen
M.E. PARROTT Memphis A.J. TALMAN Amsterdam
H.0. PEITGEN Bremen H. THIEME MHnster
H. PETERS Bonn M. TODD Ithaca
M. PREFER Bremen .G TONAR Berlin
.S RANKIN Morgantown H. TROGER Wien
N. REIF Hamburg A. TROMBA Santa Cruz
M. REICHERT Frankfurt .H UNGER Bonn
R. SAIGAL Evanston H.A. VENOBLER Portsmouth
D. SALAMON Bremen A. VIGNOLI Cosenza
D. SAUPE Bremen R. VILLELA-BRESSAN Padua
G. SEIFERT Aachen H. VOSS Hamburg
.S SESSA Neapel H.O. WALTHER MHnchen
R. SEYDEL MHnchen P. WALTMAN Iowa City
H.W. SIEGBERG Bonn H.W. WARBRUCK Bonn
.G SIMON Graz J. WEINBERG Bonn
H.L. SMITH Salt Lake City M. WILLEM Louvain-la-Neuve
J. SMOLLER Ann Arbor D. WILLIAMS College Park
D. SOCOLESCU Karlsruhe T.E. WILLIAMSON Upper Montclair
R. SOCOLESCU Karlsruhe C. ZANCO Mailand
M. SORG Stuttgart
LECTURES
J. C. ALEXANDER Numerical continuation methods - continuous and discrete
W. ALT Periodic solutions of a functional differential equation
N. ANGELSTORF Multiple periodic solutions for functional differential
equations
O. ARINO Oscillatory solutions of a delay equation
H. T. BANKS Approximation and control of functional differential
equations
.S N. CHOW .I Fuller index and existence of periodic solutions
.2 Some results on nonlinear wave equations
G. COOPERMAN Properties of s-condensing maps
E. N. DANCER Bifurcation with symmetries
B. C. EAVES Solving equations with PL-homotopies
P. M. FITZPATRICK Global bifurcation
D. FLOCKERZI Hopf bifurcation where the eigenvalue crosses the axis
with zero speed
W. FORSTER On approximating fixed points in CO,I
K. P. HADELER Delay equations in biology
J. K. HALE .I Dissipative processes
.2 Phase space for infinite delays
.3 Stability with respect to delays
×
J. IZE Some questions on bifurcation in several parameters
J. .L KAPLAN Chaotic behavior of multidimensional difference equations
R. .B KELLOGG Fixed point computations, multiple solutions, and renal
flow networks
K. KUNISCH Order preserving functional dilferential equations
G. V. D. LAAN - A restart algorithm without an artificial level for
A. J. J. TAL~N computing fixed points
T. Y. LI Numerical aspects of the continuation method
J. ~\LLET-PARET Periodic solutions of autonomous ordinary differential
equations, Ham~ltoaian systems and tile Fuller index
J. A. NOHEL A singularly perturbed functional differential equation
R. D. NUSSBAUM Periodic solutions of nonlinear functional differential
equations
M. PRUFER Calculating g|obal bifurcation
R. SAIGAL .I Piecewise linear methods for approximating fixed points
.2 Piecewise linear approximations of mappings
.3 Asymptotic behav~our of the fixed point computing
methods
J. SCHEURLE Bifurcation into k-dimensional invariant tori of quasi-
periodic solutions
K. SCHMITT Periodic solutions of forced delay equations
K. SCHUMACHER Dynamical systems with memory
R. SEYDEL Numerical computation of branch points in ordinary
differential equations
f×
J. SMOLLER A gobai bifurcation theorem
E. SPERNER . A few remarks on labelling theorems
.2 Kombinatorische Eigenschaften bewerteter Komplexe
mit Orientierung
M. J. TODD Exploiting structure in fixed point computation
A. J. TROMBA A new proof of the ~symptotic conjecture in fixed point
theory
H. O. WALTHER Instability yields periodic solutions of delay equations
by Schauder's theorem
P. WALTMAN Threshold model of antigen-antibody dynamics