On Exponential Stability of Variational Difference Equations

We prove that a general system of variational difference equations is uniformly exponentially stable if and only if certain associated sets are of the second category. We also deduce necessary and sufficient conditions for uniform exponential stability of systems with uniformly bounded coefficients. We apply our results for the study of exponential stability of linear skew-product flows, generalizing some stability theorems recently obtained in [A. L. Sasu, Math. Ineq. Appl. 7 (2004)