Flows on Homogeneous Spaces and Diophantine Approximation

齐次空间上的流和丢番图近似

• 批准号: 9704489
• 负责人: Dmitry Kleinbock
• 金额: $ 6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704489&HistoricalAwards=false
• 关键词: Flows; Homogeneous; Spaces; Diophantine; Approximation

9704489 Kleinbock This project deals with algebraic dynamical systems and their applications to number theory. Many problems concerning diophantine approximations can be cast in terms of the behavior of the orbits of a suitable homogeneous flow. Non-generic orbits such as those avoiding a given finite set or ones that remain bounded are of particular interest. The investigator is to continue his work on escapable sets and metric properties of matrices arising in diophantine approximations. Dynamical systems in the present context deal with how points in a system move over time, given a set of differential equations (or laws of nature) governing the system. It turns out that various numerical approximations used in the theory of integer equations can be better calculated once they are phrased in dynamical systems language.

9704489克莱伯克这个项目研究的是代数动力系统及其在数论中的应用。关于丢番图近似的许多问题可以用适当的均匀流的轨道的行为来表示。非一般轨道，如那些避开给定有限集或保持有界的轨道，是特别令人感兴趣的。研究者将继续研究丢番图逼近中出现的矩阵的可避集和度量性质。在目前的上下文中，动力系统处理的是系统中的点如何在给定的一组微分方程式(或自然定律)支配系统的情况下随时间移动。结果表明，整数方程理论中使用的各种数值近似，只要用动力系统语言表述，就能更好地计算。