# New Trends in Difference Equations

DOI link for New Trends in Difference Equations

New Trends in Difference Equations book

Proceedings of the Fifth International Conference on Difference Equations Tampico, Chile, January 2-7, 2000

# New Trends in Difference Equations

DOI link for New Trends in Difference Equations

New Trends in Difference Equations book

Proceedings of the Fifth International Conference on Difference Equations Tampico, Chile, January 2-7, 2000

Edited BySaber N. Elaydi, J. LopezFenner, G. Ladas, M. Pinto

Edition 1st Edition

First Published 2002

eBook Published 28 February 2002

Pub. location London

Imprint CRC Press

Pages 320 pages

eBook ISBN 9780429165290

SubjectsMathematics & Statistics

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#### Get Citation

Elaydi, S. (Ed.), LopezFenner, J. (Ed.), Ladas, G. (Ed.), Pinto, M. (Ed.). (2002). New Trends in Difference Equations. London: CRC Press, https://doi.org/10.1201/9781482265156

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,