Mathematical Sciences: Smale Flows on 3-Manifolds

Ketty de Rezavier将从事动力系统的定性理论研究。这里的主要目标是获得一个整体分类的一类流动的歧管。她将把注意力集中在所谓的斯梅尔流上。由于它们的实际应用，它们形成了一类重要的流。德Rezande将试图扩大她的一些早期工作有关斯梅尔流动的三个领域。主要的重点将是获得更一般的三个流形的结果。其目的是找到的限制的拓扑结构的歧管上的Smale流的地方。这将涉及调查到什么程度的组合条件的一定集合是必要的和足够的Smale流。

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.