Stability in Nonautonomous Dynamics: A Survey of Recent Results

Abstract

We discuss recent results in the stability theory of nonautonomousdifferential equations under sufficiently small perturbations.We mostly concentrate on the description of our own work, with emphasison the Lyapunov stability of solutions, the existence and smoothnessof invariant manifolds, and the construction and regularity of topologicalconjugacies, among other topics. The main novelty is that we alwaysconsider a nonuniform exponential behavior of the linear variationalequations, given either by the existence of a nonuniform exponentialcontraction or a nonuniform exponential dichotomy.