New criteria for exponential expansiveness of variational difference equations

The aim of this paper is to obtain general input-output conditions for uniform exponential expansiveness of variational difference equations in terms of the complete admissibility of pairs of sequence spaces. We introduce a large class Q(N) of Banach sequence spaces and we deduce the connections between the complete admissibility of the pair (B(Θ,V(N,X)),U(N,X)) with U,V∈Q(N) and the uniform exponential expansiveness of a system of variational difference equations. We apply our results at the study of the uniform exponential expansiveness of linear skew-product flows.