Mathematical Sciences: Dynamical Systems and Zeta Functions

数学科学：动力系统和 Zeta 函数

• 批准号: 8911021
• 负责人: David Fried
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8911021&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Zeta

The principal investigator will relate dynamical systems to topology and geometry using zeta functions. This project will extend his previous contributions which clarify relationships between periodic trajectory structure and the topology of the underlying space. Besides broadening this connection, the principal investigator will study analogous problems for a complex manifold which supports a holomorphic flow. The study of the relationship between shapes of surfaces and types of periodic orbits has its origins with Poincare at the turn of the century. For example, any vector field on the sphere must have a fixed point. Thus the wind cannot blow everywhere on the surface of the earth at the same time; there must be still air somewhere. The principal investigator will extend current theory which explains which kinds of periodic behavior on surfaces and higher-dimensional manifolds are permitted.

主要研究者将使用ZETA函数将动态系统与拓扑和几何形状联系起来。该项目将扩大他以前的贡献，以阐明周期性轨迹结构与基础空间的拓扑之间的关系。除了扩大这种联系外，首席研究者还将研究支持全态流的复杂流形的类似问题。对表面形状与周期性轨道类型之间的关系的研究起源于本世纪初的繁殖性。例如，球体上的任何向量场都必须具有固定点。因此，风不能同时吹到地球表面。某个地方必须有空气。主要研究者将扩展当前理论，该理论解释了允许表面上哪种周期性行为和更高维的流形。