Mathematical Sciences: Fundamental Aspects of Nonlinear Dynamics

该项目将涵盖三个相互关联的基本领域， 应用数学 第一个是大振幅 动力学中的拟周期运动和概周期运动 多自由度系统。 主要研究者 将开发新的研究方法，超越KAM 理论的小扰动，利用一种新的非线性 p.d.e. approach. 第二个相关的话题涉及漩涡 理想无粘性流体的动力学 这里的校长 调查人员将研究突出的问题， 涡环的蛙跳、涡核的分类和涡 气泡式和螺旋式破裂。 最后，校长 研究人员将研究新理论中的“通量现象” 高Tc超导，一个最重要的领域， 高技术 所有这些领域都需要深入了解 非线性科学及其相关的数学结构。 这一直是调查员研究的中心焦点 二十多年了

This project will cover three basic interrelated areas of applied mathematics. The first is concerned with large amplitude motions both quasi periodic and almost periodic in dynamical systems of many degrees of freedom. The principal investigator will develop new methods of study, going beyond the KAM theory for small perturbations, that utilize a novel nonlinear p.d.e. approach. The second related topic involves vortex dynamics of an ideal inviscid fluid. Here the principal investigator will research the outstanding problems of leapfrogging of vortex rings, classes of vortex cores, and vortex breakdown of bubble and spiral type. Finally, the principal investigator will study of "flux phenomenon" in the new theories of high Tc superconductivity, an area of prime importance in high technology. All these areas require deep understanding of nonlinear science and its associated mathematical structures. This has been the central focus of the investigator's research for over two decades.