Construction of Smooth Conjugacies

This chapter uses the machinery developed in the former chapters, together with a few other elements, to linearize via a smooth map any sufficiently small tempered perturbation of a tempered exponential dichotomy in the absence of resonances. More precisely, we show that if there are no resonances up to a given order, then the nonlinear dynamics can be linearized by local diffeomorphisms with any prescribed regularity.