Nonuniform almost reducibility of nonautonomous linear differential equations

Abstract

We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be written as diagonal system with a perturbation which is small enough. Moreover we show that the diagonal terms are contained in the nonuniform exponential dichotomy spectrum. For this purpose we introduce the concepts of nonuniform almost reducibility and nonuniform contractibility which are generalizations of these notions originally defined in a uniform context.