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 Singapore • New Jersey • London • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 9128 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. DYNAMICAL SYSTEMS AND APPLICATIONS Copyright © 1995 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, Massachusetts 01923, USA. ISBN 981-02-2383-8 This book is printed on acid-free paper. Printed in Singapore by Uto-Print 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) This page is intentionally left blank 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 This page is intentionally left blank 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