Dynamical systems and applications

693 Pages·1995·22.77 MB·English

by  Agarwal R.P. (ed.)

DYNAMICAL
SYSTEMS
AND
APPLICATIONS
WORLD SCIENTIFIC SERIES IN APPLICABLE ANALYSIS
Editor
Ravi P. Agarwal (National University of Singapore)
Advisory Board
J. M. Ball (Heriot-Watt Univ.)
Shui-Nee Chow (Georgia Inst. Tech.)
R. P. Gilbert (Univ. Delaware)
P. J. van der Houwen (Stichting Math. Centrum)
Junji Kato (Tohoku Univ.)
V. Lakshmikantham (Florida Inst Tech.)
Masatake Mori (Univ. Tokyo)
M. Z. Nashed (Univ. Delaware)
Wolfgang Walter {Univ. Karlsruhe)
Vol. 1: Recent Trends in Differential Equations
ed. R. P. Agarwal
Vol. 2: Contributions in Numerical Mathematics
ed. R. P. Agarwal
Vol. 3: Inequalities and Applications
ed. R. P. Agarwal
Vol. 4: Dynamical Systems and Applications
ed. R. P. Agarwal
Forthcoming
Vol. 5: Recent Trends in Optimization Theory and Applications
ed. R. P. Agarwal
World Scientific Series in Applicable Analysis
Volume 4
Editor
R.P.Agarwal
Department of Mathematics
National University of Singapore
DYNAMICAL
SYSTEMS
AND
APPLICATIONS
World Scientific
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British Library Cataloguing-in-Publication Data
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DYNAMICAL SYSTEMS AND APPLICATIONS
Copyright © 1995 by World Scientific Publishing Co. Pte. Ltd.
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V
Contributors
B.Abraham-Shrauner (U.S.A) N.V.Minh (Vietnam)
V.Affaimovich (U.S.A.) V.Mioc (Romania)
N.U.Ahmed (Canada) K.Mischaikow (U.S.A.)
B.Aulbach (Germany) M.Misiurewicz (U.S.A.)
E.J.Avila-Vales (Mexico) J.W.Mooney (U.K.)
F.Battelli (Italy) M.E.Muldoon (Canada)
J.M.Blazquez (Chile) S.Murakami (Japan)
L.Block (U.S.A.) M.Muraskin (U.S.A.)
T.A.Burton (U.S.A.) A.D.Myshkis (Russia)
R.S.Cantrell (U.S.A.) F.Neuman (Czech Republic)
C.Y.Chan (U.S.A.) J.C.Newby (U.K.)
P.Collet (France) Y.Nishiura (Japan)
R.Cushman (Holland) Z.Nitecki (U.S.A.)
M.Denker (Germany) M.Ohta (Japan)
F.N.Diacu (Canada) G.Osipenko (Russia)
Y.H.Ding (P.R.China) N.Ozalp (Turkey)
N.S.A.El-Sharif (U.K.) M.Pollicott (U.K.)
J.E.Fornaess (U.S.A.) Min Qu (U.S.A.)
M.Frankel (U.S.A.) Donal O'Regan (Ireland)
R.Galeeva (U.S.A.) E.Romanenko (Ukraine)
A.Galves (Brasil) V.Roytburd (U.S.A.)
V.Gershkovich (Australia) L.Shaikhet (Ukraine)
M.Girardi (Italy) J.Shidawara (Japan)
L.Gotusso (Italy) N.Sibony (France)
J.Graczyk (U.S.A.) W.-H.Steeb (South Africa)
Y.Hino (Japan) C.Stoica (Romania)
I.Hoveijn (Holland) G.Swiatek (U.S.A.)
V.Hutson (U.K.) T.Takaishi (Japan)
P.B.Kahn (U.S.A.) N.D.Thai Son (Vietnam)
J.Kato (Japan) R.Triggiani (U.S.A.)
J.Keesling (U.S.A.) A.E.Tuma (Chile)
S.Keras (U.K.) E.H.Twizell (U.K.)
V.Kolmanovskii (Russia) M.Urbanski (U.S.A.)
I.Komarchev (Russia) T.D.Van (Vietnam)
J.Komornik (Slovakia) A.Vanderbauwhede (Belgium)
I.Lasiecka (U.S.A.) A.Veneziani (Italy)
N.D.Liem (Vietnam) G.Vickers (U.K.)
J.Lopez-Gomez (U.K.) X.Xiang (P.R.China)
R. Ma (P.R.China) T.Young (U.S.A)
I.Melichercik (Slovakia) Y.Zarmi (Israel)
A.Mingarelli (Canada)
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vii
Preface
World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting
new developments of high mathematical standard and current interest. Each
volume in the series shall be devoted to the mathematical analysis that has
been applied or is potentially applicable to the solutions of scientific, engineer­
ing, and social problems. For the past twenty five years, there has been an ex­
plosion of interest in the study of nonlinear dynamical systems. Mathematical
techniques developed during this period have been applied to important non­
linear problems ranging from physics and chemistry to ecology and economics.
All these developments have made dynamical systems theory an important
and attractive branch of mathematics to scientists in many disciplines. This
rich mathematical subject has been partially represented in this collection of
45 papers by some of the leading researchers in the area. The editor is grateful
to his colleague Lawrence Ma for his help in the preparation of this volume.
R.P.Agarwal
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ix
CONTENTS
Preface vii
Lie Symmetries, Hidden Symmetries and Time-Dependent Invariants 1
B. Abraham-Shrauner
Generalization of a Theorem of Malta and Palis 11
V. Afraimovich and T. Young
Necessary Conditions of Optimality for a Class of Semilinear
Uncertain Systems with Unbounded Monotone Operator 27
TV. U. Ahmed and X. Xiang
Semigroups and Exponential Stability of Nonautonomous Linear
Differential Equations on the Half-Line 45
B. Aulbach and N. V. Minh
Permanence in Periodic-Parabolic Ecological Systems with Spatial
Heterogeneity 63
E. J. Avila-Vales and R. S. Cantrell
Exponential Bounds for Bifurcation Functions in Singular Systems
with Impulses 77
F. Battelli
Bifurcation from Homoclinic Orbits to a Saddle-Saddle Point in a
Banach Space 91
J. M. Bldzquez and A. E. Tuma
Continuity of Entropy for a Two-Parameter Family of Bimodal Maps 101
L. Block, R. Galeeva and J. Keesling
The Search for Periodic Solutions in Neural Networks 117
T. A. Burton
Singular Reaction-Diffusion Mixed Boundary-Value Quenching
Problems 127
C. Y. Chan and N. Ozalp
Asymptotic Distribution of Entrance Times for Expanding Maps
of the Interval 139
P. Collet and A. Galves
X
Visualizing Special Motions of the Euler Top 153
R. Cushman and I. Hoveijn
Conforms! Measures and 5-Unimodal Maps 169
M. Denker, Z. Nitecki and M. Urbanski
The Manev Two-Body Problem: Quantitative and Qualitative
Theory 213
F. N. Diacu, A. Mingarelli, V. Mioc and C. Stoica
Periodic Solutions for a Second Order Hamiltonian System 229
Y. H. Ding and M. Girardi
Holomorphic Symplectomorphisms in C2 239
J. E. ForncBss and N. Sibony
On a Free Interface Problem Modeling Solid Combustion and
Rapid Solidification in Infinite Medium 263
M. Frankel, M. Qu and V. Roytburd
On Simplest Engel Structures on 4-Manifolds 279
V. Gershkovich
Discrete and Continuous Nonlinear Models for the Vibrating String 295
L. Gotusso and A. Veneziani
Polynomial-Like Mappings Induced by Real Polynomials 315
J. Graczyk and G. Swiatek
Stability Properties in a Abstract Linear Functional Differential
Equations with Infinite Delay 329
Y. Hino and S. Murakami
Limit Behaviour for a Competing Species Problem with Diffusion 343
V. Hutson, J. Lopez-Gomez, K. Mischaikow and G. Vickers
Normal Form Perturbation Analysis of Non-Autonomous
Oscillatory Systems 359
P. B. Kahn and Y. Zarmi
On the Compact Asymptotic Stability 375
J. Koto
Spurious Chaotic Solutions of Differential Equations 385
5. Keras