Ketty de Rezende will work in the qualitative theory of dynamical systems. The main objective here is to obtain a global classification of a class of flows on a manifold. She will focus her attention on the so-called Smale flows. These form an important class of flows because of their practical applications. De Rezende will try to extend some of her earlier work concerning Smale flows on the three sphere. The main focus will be to obtain results on more general three manifolds. The aim is to find the restrictions which the topology of the manifold places on a Smale flow. This will involve investigating to what extent a certain collection of combinatorial conditions is necessary and sufficient for a Smale flow.
