Mathematical Sciences: Dynamical Systems and Smooth Ergodic Theory

主要研究人员将继续在 动力系统的混沌行为。特别是他们将 研究Henon和标准地图， 一维非一致椭圆双曲组的例子 两个.遗嘱试图证明混乱行为的存在 证明了李雅普诺夫指数的正性他们还将 研究复杂动力学中的Julia集，特别是 非均匀双曲情形 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 research in the chaotic behavior of dynamical systems. In particular they will study the Henon and standard maps which are the prototypical examples of nonuniformly elliptic hyperbolic systems in dimension two. The will attempt to prove the existence of chaotic behavior by proving the positivity of Lyapunov exponents. They will also study the Julia sets in complex dynamics, particularly in the nonuniform hyperbolic case. 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.