Ergodic and Statistical Phenomena in Dynamics

动力学中的遍历和统计现象

• 批准号: 0600996
• 负责人: Yakov Sinai
• 金额: $ 31.85万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600996&HistoricalAwards=false
• 关键词: Ergodic; Statistical; Phenomena; Dynamics

Three projects are proposed. The first one is on a new approach to the analysis of the dynamics described by the three-dimensional Navier-Stokes system. Such system is being considered as an infinite dimensional dynamical system in Fourier space. The second one is on ergodic properties of internal exchange transformations, in particular the properties of weak mixing of flows on two-dimensional surfaces and their applications, especially to number theory. The last project is on the statistical version of the (3x+1)-problem. The development of mathematical theory of Navier-Stokes system can lead to better understanding of mechanisms of development of singularities in other important non-linear systems of equations, in particular, the prediction of tornados. The (3x+1)-problem will have connections and applications to number theory. The PI will also actively involve in training and mentoring graduate students and postdoctoral associates.

提出了三个项目。第一个是关于三维N-S系统描述的动力学分析的一种新方法。这种系统被认为是傅立叶空间中的无限维动力系统。二是关于内部交换变换的遍历性质，特别是二维表面上流动的弱混合的性质及其应用，特别是在数论方面。最后一个项目是关于(3x+1)-问题的统计版本。发展Navier-Stokes系统的数学理论可以更好地理解其他重要的非线性方程组奇点的发展机制，特别是龙卷风的预报。(3x+1)-问题将与数论有联系和应用。PI还将积极参与对研究生和博士后助理的培训和指导。