New criteria for exponential stability of variational difference equations

The aim of this work is to obtain very general characterizations for uniform exponential stability of variational difference equations, using Banach sequence spaces. We prove that a system of variational difference equations is uniformly exponentially stable if and only if there is a Banach sequence space BB, with certain properties, such that the set of all vectors with the corresponding orbits contained uniformly in BB is of the second category. We apply our result at the study of the uniform exponential stability of linear skew-product flows.