Nonuniform contractions and converse stability results via a smooth topological equivalence

Abstract

Given a nonautonomous linear system of ordinary differential equations with nonuniform contractions on the half line, we study the smoothness and preserving orientation properties of a global linearization between this system and a family of nonlinear perturbations. As an application of the previous study, we improve a converse stability result for the nonlinear system in terms of density functions.