Mathematical Sciences: Hamiltonian Dynamics

数学科学：哈密顿动力学

• 批准号: 9627979
• 负责人: Christophe Gole
• 金额: $ 4万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9627979&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hamiltonian; Dynamics

9627979 Gole This project uses variational techniques to prove the existence of orbits of many different topological types in conservative dynamical systems. In addition, the investigator will consider the method of frequency analysis introduced by J. Lasker and apply them to detect chaos and diffusion in conservative systems. One of the proposed goals is to give a firm mathematical foundation of Lasker's method, which at present is mostly a numerical method. Chaos and diffusion phenomena in dynamical systems have wide ranging applications in the physical world. For example, they can be used to model certain weather systems involving turbulence and sudden bifurcation.

9627979 Gole 该项目使用变分技术来证明保守动力系统中许多不同拓扑类型的轨道的存在。此外，研究者将考虑J. Lasker引入的频率分析方法，并将其应用于检测保守系统中的混沌和扩散。提出的目标之一是为拉斯克方法提供坚实的数学基础，目前拉斯克方法主要是一种数值方法。 动力系统中的混沌和扩散现象在物理世界中具有广泛的应用。例如，它们可用于模拟某些涉及湍流和突然分叉的天气系统。