Estabilidade de Lyapunov em fibrados

Abstract

In this work, we present some results on Lyapunov stability for semigroup actions on principal and associated bundles. We introduce the concept of orbit preserving map and study the behavior of stable sets and attractors under such maps. We use the results obtained for orbit preserving maps to study stable sets and attractors in the setting of principal and associated bundles. In addition, we present some result that relate stable sets and attractors in the total space of an associated bundle to the corresponding concepts in the fibers. Finally, we relate the concepts of stable sets and attractors for the zero section of a vector bundle in the context of n-time semiflows and control systems