Dynamics of Partially Hyperbolic Systems

部分双曲系统的动力学

• 批准号: 0408704
• 负责人: Keith Burns
• 金额: $ 9.95万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0408704&HistoricalAwards=false
• 关键词: Dynamics; Partially; Hyperbolic; Systems

Burns proposes to study partially hyperbolic dynamical systems. He will focus on the time-one map of the frame flow, on compact group extensions of hyperbolic basic sets, and on extensions of the Pugh-Shub theorems. The proposed research will contribute to the understanding of partial hyperbolicity, a far-reaching extension of one of the basic paradigms in the study of chaotic systems, namely, uniform hyperbolicity. The results of the research will be broadly disseminated in the scientific literature and in lectures. This work will also contribute to the mathematical formation of graduate students at Northwestern, in part by lectures of the PI, and in part by students working on this and related subjects under his guidance.

伯恩斯提议研究部分双曲动力系统。他将重点研究框架流的时间一映射、双曲基本集的紧群扩展以及 Pugh-Shub 定理的扩展。拟议的研究将有助于理解部分双曲性，这是混沌系统研究的基本范式之一（即均匀双曲性）的深远延伸。研究结果将在科学文献和讲座中广泛传播。 这项工作也将有助于西北大学研究生的数学形成，部分是通过 PI 的讲座，部分是通过在他的指导下从事该学科和相关学科的学生。