Mathematical Sciences: Ergodic Theory and Related Topics

数学科学：遍历理论及相关主题

• 批准号: 9500803
• 负责人: Jacob Feldman
• 金额: $ 2.4万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500803&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Ergodic; Theory; Related

9500803 Feldman This project involves many facets of work on probability theory and ergodic theory. The research includes work on the following projects: A classification of filtrations of stochastic processes; Zero-one asymptotic properties of averages of functions transformed under ergodic measure preserving transformations; Cofiltrations and ergodic group actions; Reparametrization for Euclidean group actions and for foliations; Ergodic properties of multiplication on the circle. Collectively, these projects cover a broad portion of the current ergodic theory research landscape. Ergodic theory in general concerns understanding the average long-term behavior of systems that are too complicated or chaotic to be followed in real time. Under the heading of "dynamics" can be placed the modern theory of how repeated applications of transformations effect measurable quantities. In this way, groups of transformations and abstract measure theory form the mathematical cornerstones of ergodic theory. This proposal involves the leading edge of the mathematics of ergodic theory. ***

9500803费尔德曼这个项目涉及到概率论和遍历理论的许多方面的工作。该研究包括以下项目的工作：随机过程的过滤分类;在遍历测度保持变换下变换的函数平均值的零-一渐近性质;共过滤和遍历群作用;欧几里德群作用和叶理的重新参数化;在圆上乘法的遍历性质。总的来说，这些项目涵盖了当前遍历理论研究领域的广泛部分。 遍历理论一般涉及理解系统的平均长期行为，这些系统过于复杂或混乱，无法在真实的时间内遵循。在“动力学”的标题下，可以放置关于变换的重复应用如何影响可测量量的现代理论。这样，变换群和抽象测度理论就构成了遍历理论的数学基石。这个建议涉及到遍历理论的数学前沿。 ***