New criteria for exponential expansiveness of variational difference equations

Abstract

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.