Mathematical Sciences: Analytic and Numerical Studies of Long Term Behavior

数学科学：长期行为的分析和数值研究

• 批准号: 9201143
• 负责人: Rafael de la Llave
• 金额: $ 9.43万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201143&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytic; Numerical; Studies

De la Llave will study the long term behavior of deterministic systems appearing in practical problems. The methods proposed for this study are usually based in finding landmarks that organize the long term behavior. Since these landmarks satisfy complicated functional equations, part of this project is devoted to the analytical study of these non-local functional equations. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

德拉拉夫将研究出现在实际问题中的确定性系统的长期行为。为这项研究提出的方法通常基于寻找组织长期行为的地标。由于这些地标满足复杂的函数方程，本项目的一部分致力于这些非局部函数方程的分析研究。这个项目涉及对遍历理论的研究。一般说来，遍历理论涉及理解系统的平均行为，这些系统的动力学太复杂或太混乱，以至于无法在微观细节上进行跟踪。在“动力学”的标题下，可以把一组抽象的变换如何作用于光滑空间的现代理论放在下面。通过这种方式，遍历理论在寻求对均匀空间上的流动进行分类的过程中与几何相联系。