Alexandre N. Oliveira Sousa

Universidade Federal de Santa Catarina, Brazil

Title: Inertial manifolds and its complementary stable manifolds and robustness of exponential splitting

Abstract: We investigate the existence of invariant manifolds for non-autonomous differential equations, focusing in particular on inertial and stable manifolds.   We provide conditions involving a gap condition and the size of the perturbation to ensure that  exponential splitting is robust under nonlinear perturbations, which gives the existence of the desired manifolds. We also establish a characterization of both types of manifolds in terms of the space of solutions exhibiting a common growth behavior, analogous to the classical characterizations involving exponential dichotomies.