On the stability in periodic and almost periodic difference systems

On the Stability in Almost Periodic Discrete Systems

In this paper, the discrete system which is described by difference equations xn+1 = fn(xn), fn(0) = 0, n = 0, 1, 2, . . . . is considered. This system has the trivial (zero) solution xn = 0. Sufficient conditions of its asymptotic stability are obtained in the cases when functions fn(x) are almost periodic in n. Copyright c ©2005 IFAC

Almost Periodic and Periodic Solutions of Difference Equations

I t is easy to see that for every point (y, N) in WXI there is a solution (n) of (1) that satisfies <1>(N) =y. This solution is defined and unique on some set N^nKN*» where N<» is maximal. (That is, either iV» = °o or ^ i V ^ — l) (£W.) The solution may or may not be continuable for nƒ> rc)> 0^w<iV o o(^ , / ) , be the soluti...

Finite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures

Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We...

Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional Difference Equations in Phase Spaces

On Hartman Almost Periodic Functions

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...