Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations PDF
Preview Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations
Communications in Difference Equations Professor Jerzy Popenda (1948-1999) Communications in Difference Equations Proceedings of the Fourth International Conference on Difference Equations Poznan, Poland August 27-31, 1998 Edited by s. Elaydi Trinity University, San Antonio, Texas, USA G. Ladas University ofR hode Island, Kingston, USA J. Popendat and J. Rakowski Poznan University of Technology, Poland Gordon and Breach Science Publishers Australia· Canada· France· Germany· India· Japan· Luxembourg· Malaysia· The Netherlands· Russia· Singapore· Switzerland CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2000 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140513 International Standard Book Number-13: 978-1-4822-8333-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To Professor Jerzy Popenda Born in Poland, Professor Popenda received his PhD degree in at Adam Mickiewicz University in 1980 Poznan and his postdoctoral degree in He worked 1991. at Poznan University of Technology as a research fellow from until his death in and published more 1971 1999 than research papers in various fields of mathematics, 60 including recurrence equations and inequalities, discrete modeling, dynamical systems, oscillations and stability problems. An excellent educator, Professor Popenda promoted two PhD holders and reviewed other numerous dissertations as well as articles and monographs from all over the world. Besides his professional activity, he shared with us his artistic passion -especially in music and painting. TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk CONTENTS Preface xi List of Contributors xiii UNIVERSAL FUNCTIONS ON COMPLEX SPECIAL LINEAR GROUPS Yuldtaka Abe 1 BRANCHING RANDOM WALK WITH A SINGLE SOURCE S. Albeverio, L. V. Bogachev and E. B. Yarovaya 9 DIFFERENCE EQUATIONS IN GROUPS Anna Andruch-Sobilo and Jerzy Popenda 21 GEOMETRY OF FIRST INTEGRALS FOR 2ND ORDER DIFFERENCE EQUATIONS Leon A"iola, Frederick Cleaver and Thomas Gruszka 35 BEHAVIOR OF SOLUTIONS OF PERTURBED QUASILINEAR DIFFERENCE EQUATIONS R. Arul, E. Thandapani, John R. Graef and Paul W. Spikes 45 IDENTITIES FOR ORTHOGONALITY AND APPLICATIONS A. L. W. Von Bachhaus 59 ON THE NONAUTONOMOUS DIFFERENCE EQUATION Xn.,= max{xn• An} XnXn-, W. J. Briden. G. Ladas and T. Nesemann 73 CENTRAL LIMIT THEOREMS FOR LINEAR, NONLINEAR AND MIXING PROCESSES Kamal C. Chanda 79 INVITATION TO PARTIAL DIFFERENCE EQUATIONS Sui Sun Cheng 91 viii CONTENTS RETRACT PRINCIPLE FOR DIFFERENCE EQUATIONS J. Diblik 107 ON A PHASE PATTERN STRUCTURE OF UNIMODAL 2-ENDOMORPHISMS Vladimir A. Dobrynskiy 117 TRIGONOMETRIC TRANSFORMATION AND OSCILLATORY PROPERTIES OF SECOND ORDER DIFFERENCE EQUATIONS Ondre} Dosly 125 ON GLOBAL BIFURCATION THEORY OF POLYNOMIAL DYNAMICAL SYSTEMS AND ITS APPLICATIONS Valery A. Gaiko 135 GLOBAL STABILITY IN SOME POPULATION MODELS E. A. Grove, C. M Kent, G. Ladas, R. Levins and S. Valicenti 149 RECURRENCE EQUATIONS IN SOLVING OPERATOR EQUATIONS OF THE SPECIAL TYPE Lechoslaw H",cia 177 ON DISCONJUGACY FOR VECTOR LINEAR HAMILTONIAN SYSTEMS ON TIME SCALES Roman Hilscher 181 A NOTE ON THE ASYMPTOTIC PROPERTIES OF SOME NONAUTONOMOUS MATRIX DIFFERENCE EQUATIONS Sophia R. J. -Jang 189 A GENERALIZATION OF THE MILLOUX-HARTMAN THEOREM FOR NONLINEAR SYSTEMS Janos Karsai, John R. Graef and Michael Y. Li 203 SPATIAL DISCRETIZATION OF PULLBACK ATTRACTORS OF NONAUTONOMOUS DIFFERENCE EQUATIONS P. Kloeden 215 CONTENTS ix A DISCRETE NONLINEAR AND NON-AUTONOMOUS MODEL OF CONSENSUS FORMATION U. Krause 227 TRAJECTORIES FOR THE CASE OF A RATIONAL SYSTEM OF DIFFERENCE EQUATIONS Ewa Magnucka-Blandzi 237 APPLYING THE SYSTEM DERIVE TO INVESTIGATE THE TRUNCATION RELATED TO THE MONOMIALS DEFINED ON THE SET OF NATURAL NUMBERS Adam Marlewski and Jerzy Popenda 247 ANALYSIS OF INFLUENCE OF SELECTED PARAMETERS ON THE BEHAVIOUR OF THE DISCRETE LOGISTIC EQUATION Szymon Jerzy Miedziejko and Jerzy Ryszard Popenda 253 ASYMPTOTIC BEHAVIOUR OF OSCILLATORY SOLUTIONS OF A SECOND ORDER DIFFERENCE EQUATION J. Mikolajski 265 CHAOTIC BIFURCATIONS ALONG ALGEBRAIC CURVES K. Nishizawa and M Fujimura 273 DISCRETE APPROXIMATIONS AND COMPUTER INVESTIGATIONS OF ISOLATED INVARIANT SETS Douglas E. Norton 283 SEMI-HYPERBOLICITY AND INVERSE SHADOWING Jerzy Ombach 291 FUNDAMENTAL SOLUTIONS FOR INFINITE DISCRETE BEAMS ON ELASTIC FOUNDATION Zdzislaw Pawlak and Jerzy Rakowski 301 DISCRETE CLASSICAL ORTHOGONAL POLYNOMIALS AND INTERFEROMETRY V. Petinovti and A. LukS 311
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