ABSTRACT
This series on the International Conference on Difference Equations and Applications has established a tradition within the mathematical community. It brings together scientists from many different areas of research to highlight current interests, challenges and unsolved problems. This volume comprises selected papers presented at the Fifth Interna
TABLE OF CONTENTS
chapter |1 pages
On the Subtle Role oflnvertibility in Discrete Dynamics
Abstract We consider two of the most fundamental topics in
chapter |1 pages
of 35 Theorem 2.1: C
R" on an R"- of a fixed point p of f and that the derivative of f at p invertible and no eigenvalue" with modultu 1. That this theorem does not hold without the invertibility as- f of Theorem 2.1 is seen to be topologically conjugate to u(A-) of A+ and A-, respectively, > 1} and u(A-) {A E : 0 < <
chapter |1 pages
where the functions s+, and sare continuous and vanish at 0.
Example: We consider the mapping w) : the w-axis h: .N-+ := h(.N) is
chapter |1 pages
ofl nvertibility in Discrete Dynamics is a homeomorphism we get the inclusion (0, 0, 0) E int J(N). This,
:= {(0, 0)} x ( -2e, 2e) to the boundary g('P) \ int g('P) of the cylinder g('P). From (g('P)\intg('P)) =
chapter |1 pages
Theorem 2.2: Coruider a C : n n-
of the coordinate origin and that I of top. Furthermore, are tangent to the of the linearization DIP.
chapter |1 pages
(i) Hypothesis on linear part: The evolution operators and
B( k) y( k ), respectively, satisfy the estimates < K1alc-l for all k k, l I, < K2fJic-l for all k I, IE I ofF and are ... , m} have := sup (k, x, y) < oo, IGin:= sup <oo.
chapter |1 pages
assume that the number 1 lies between the growth rates a and
part of system (3.1) are only supposed to lie in £(X) (and not Theorem 3.2: We consider system (9.1} satisfying the above hy- {k E 7l : k for some E s : I x X -+ graphS:= E I,e EX}, pseudo- ..\(·; lt,e,TJ) (X x Y)}. of system of the invariance equation e)+ e)) x X, Y ·) : Y
chapter |1 pages
a+u 1 then ·) : -+ Y m-time"
Y-+ := (a+ u,{3- e, '7) E R we have (k, e, E R for of the invariance + 1, + -
chapter |1 pages
A Spectral Theory for Nonautonomous Difference Equations
ofM athematics, University ofA ugsburg,
chapter |1 pages
Improvements in Asymptotic Formulae Results for Functional Difference Equations
+ B(n)y(n
chapter |1 pages
Theorem 1 Suppose that for the system ( 10) there is an eigenvector v such
=< v > and therefore {-r,-r+1, , -1,0} andB,f: NxFr i,l!!,
chapter |4 pages
n. x n. Jordan matrices
k+l,···,N > 0 B, + v• l!!,.x•uf' Improvement of Theorem Band consequences
chapter |1 pages
Necessary and Sufficient Oscillation Criteria for Discrete Reaction-Diffusion Equations
ofM athematics, Tsing Hua University,
chapter 2|1 pages
The generating matrix
= + EN, = N-+ VI r = {/: N-+ VI < oo}, = EN}. > 0, then this solution can be extended to the set
chapter I|2 pages
, is
+ + a3y3(n), f.':, then a generating matrix of Eq. ( in S is = -2-n + f.': may consider the generating matrix
chapter |12 pages
Linear ODE's for Describing
Modulators, Filter Design and Error Estimations ofM athematics, Technical University ofR menau,
chapter |1 pages
<-land a-ldl > LetQ=
if Q -+ R is a continuous map such that lg(:r, I of (-1,0) and (0,1], o· c
chapter |1 pages
'• is either L or R, then there is a 10lution such that x, '•·
s:,, x, E E s:l, Sic = c = .st' Si L, R. that(. ..
chapter |4 pages
If(.t,):-ao any sequence such
each"' Lor R, then there solution that z, e "•· 5. References
chapter i|1 pages
= 1,2, ... ,T, = maxiDIJ/(x,a)l, L = maxiD!f(x,a)l, =
... + 6a-r) this p = (xc + 6xt, + 6x2, ... , + 6x-r) of 6xt =
chapter 3|2 pages
3 Two-dimensional map with hyperbolic attracto r
< 1, < be a square in the plane (x, y). Qare presented as a separation by the function {(x,y)EQ: y<h(x)}, {(x,y)EQ: y>h(x)}. T: (x, y) f(x, y), <ax, >ax, < The Belykh map is remarkable for the fact that it has a
chapter 0|1 pages
< < 1, 0 < 2 < 2/(1 + jal), lal < 1. Finally, for
< 1/2. Thus, for a hyperbolicity get the following inequalities:
chapter |2 pages
satisfies the inequality where (I) the functions [0, oo) --+ (0, oo), 1 $ i $ p, are continuous
z+ --+ and : z+ --+ [d, are functions, c is a > 0, 1 $ i $ and wi-l are their Theorem A Let and assume (I) and (II) hold. Let z+ such that
chapter |2 pages
m) be a fundamental matrix corresponding to the
< oo. If Mu(no) < then by Theorem A it that w,-[W,(<pp-l(c))
chapter |4 pages
If the
solutions with initial conditions small enough, namely, Theorem 4. Assume that the assumptions (ii) a.nd (iii) of The- <cis
chapter 4|4 pages
EXTENSIONS In this section, our objetive is to extend some of the results to discrete systems of the form
z+; and I : z+ =-TN, -TN+ 1, · · · G!+lA;(s).
chapter |16 pages
On Convergence of Discrete Stochastic
Approximation Procedures ofM aths/CScience, oft he West Indies,
