Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 324273, 18 pages
doi:10.1155/2009/324273
Research Article

On Exponential Dichotomy of Variational Difference Equations

Bogdan Sasu

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, C. Coposu Blvd. Number 4, 300223 Timişoara, Romania

Received 23 June 2009; Revised 8 September 2009; Accepted 15 October 2009

Academic Editor: Leonid Berezansky

Copyright © 2009 Bogdan Sasu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give very general characterizations for uniform exponential dichotomy of variational difference equations. We propose a new method in the study of exponential dichotomy based on the convergence of some associated series of nonlinear trajectories. The obtained results are applied to difference equations and also to linear skew-product flows.