Mathematical Sciences: Smale Flows on 3-Manifolds

Ketty de Rezende将研究动力系统的定性理论。本文的主要目的是得到流形上一类流的全局分类。她将把注意力集中在所谓的小流量上。由于它们的实际应用，它们形成了一类重要的流。De Rezende将尝试扩展她早期关于三球面上的小流的工作。主要的重点将是获得更一般的三流形的结果。目的是找出流形的拓扑结构对小流的限制。这将涉及调查某种组合条件的集合在多大程度上对小流量是必要和充分的。

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.