Mathematical Sciences: Differentiable Dynamical Systems

主要研究人员将继续研究问题， 在动力系统和微分几何中。博恩斯教授 将研究黎曼流形上的测地线流， 曲率和构造度量的问题， 流是遍历的。弗兰克斯教授将专注于动态的 曲面的同胚，特别是面积保持 同胚罗宾逊教授将重点讨论 在更高的维度流动的猜想。他还将继续 他对“Smale”形成过程中的分叉的研究 马蹄铁”。 该奖项将支持一般领域的研究， 动力系统一个非常简单和容易的过程， 局部理解会变得非常复杂，非线性， 很难在全球范围内进行分析。动力系统是研究 从本地到全球的关系。许多物理系统可以 最好是用这一领域的数学建模，包括流体 流动和湍流，复杂的生物系统，机械 系统和化学反应。

The principal investigators will continue work in problems in dynamical systems and differential geometry. Professor Burns will study geodesic flows on Riemannian manifolds of negative curvature and the problem of constructing metrics whose geodesic flow is ergodic. Professor Franks will focus on the dynamics of homeomorphisms of surfaces and in particular, area preserving homeomorphisms. Professor Robinson will focus on the stability conjecture for flows in higher dimensions. He will also continue his study of the bifurcations in the formation of the "Smale horseshoe". This award will support research in the general area of dynamical systems. A process which is very simple and easy to understand locally can become extremely complicated, nonlinear, and difficult to analyze globally. Dynamical systems is the study of this local to global relationship. Many physical systems can best be modeled using this area of mathematics including fluid flow and turbulence, complex biological systems, mechanical systems, and chemical reactions.