Nonuniform Almost Reducibility of Nonautonomous Linear Differential Equations

We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be expressed 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 $\mathit{\text{nonuniform}}\mathit{\text{almost}}\mathit{\text{reducibility}}$ and $\mathit{\text{nonuniform}}\mathit{\text{contractibility}}$ which are generalization of this notions originally defined in a uniform context.