Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 140369, 16 pages
doi:10.1155/2009/140369

On dichotomous behavior of variational difference equations and applications

Abstract

We give new and very general characterizations for uniform exponential dichotomy of variational difference equations in terms of the admissibility of pairs of sequence spaces over ℕ with respect to an associated control system. We establish in the variational case the connections between the admissibility of certain pairs of sequence spaces over ℕ and the admissibility of the corresponding pairs of sequence spaces over ℤ. We apply our results to the study of the existence of exponential dichotomy of linear skew-product flows.