Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations

448 Pages·2000·20.506 MB·English

by  Saber N. Elaydi, Jerry Popenda, Jerry Rakowski

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. Reasonable
efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication
and apologize to copyright holders if permission to publish in this form has not been obtained. If any
copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information stor-
age or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copy-
right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222
Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro-
vides licenses and registration for a variety of users. For organizations that have been granted a photo-
copy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
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