Ergodic Phenomena in Differential Dynamics

微分动力学中的遍历现象

• 批准号: 0070698
• 负责人: Yakov Sinai
• 金额: $ 27.52万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070698&HistoricalAwards=false
• 关键词: Ergodic; Phenomena; Differential; Dynamics

One of the main problems in the Differential Dynamics is the analysis of dynamical systems with non-uniform hyperbolic behaviour. In this connection D. Kosygin and I work on the construction of standard maps without KAM-islands. Another problem which is an essential part of the proposal is to study Navier-stokes equations with random forcing and to investigate properties of their stationary distributions. One of the main problems in the theory of chaos and differential dynamics is to study dynamical systems with the mixture of regular and chaotic behaviour. One part of the proposal is devoted to the study of a big class of such systems which includes the famous standard map. I am also planning to work on various problems of mathematical and statistical hydrodynamics.

微分动力学的主要问题之一是分析具有非一致双曲行为的动力系统。 在这方面，D。柯西金和我致力于构建没有卡姆群岛的标准地图。 另一个问题是该提案的重要组成部分，它是研究具有随机强迫的Navier-Stokes方程并研究其平稳分布的性质。混沌和微分动力学理论的主要问题之一是研究具有规则和混沌混合行为的动力系统。 其中一部分的建议是专门研究的一大类这样的系统，其中包括著名的标准地图。 我还计划工作的各种问题的数学和统计流体力学。