Exponential dichotomies in average for flows and admissibility

Abstract

For a measurable cocycle over a flow or a semiflow acting on $L^1$ functions, we consider the general notion of an exponential dichotomy in average and we characterize it in terms of an admissibility property. As a nontrivial application, we establish in a simple manner the robustness of the notion under sufficiently small linear perturbations, both for cocycles over a flow and a semiflow.