Mathematical Sciences: Topics in Ergodic Theory and Dynamical Systems

数学科学：遍历理论和动力系统主题

• 批准号: 9113642
• 负责人: Jacob Feldman
• 金额: $ 7.15万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9113642&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Ergodic; Theory

Professor Feldman will continue his research in ergodic theory giving particular attention to the following areas: (i) normal distributions with respect to p,q multiplication, (ii) continuous products of probability spaces, (iii) ergodic theory for actions of amenable (non-unimodular) groups, (iv) smooth ergodic theory, and (v) subrelations of ergodic equivalence relations. Research in ergodic theory involves trying to understand 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. Another important theme in ergodic theory is the classification of systems into broad categories which are mathematically identical in an abstract sense. Professor Feldman's research will make contact with these areas.

费尔德曼教授将继续他在遍历 特别注意以下方面的理论：（一） 关于p，q乘法的正态分布，（ii） 概率空间的连续乘积，（iii）遍历理论 对于顺从（非幺模）群的作用，（iv）光滑 遍历理论，（v）遍历等价的子关系 关系 遍历理论的研究涉及试图理解 动力学过于复杂的系统的平均行为，或 混沌的微观细节。 标题下 “动力学”可以被放在现代理论中， 抽象变换作用于光滑空间。 另一个重要 遍历理论的主题是将系统分类为 在数学上完全相同的大类， 抽象的感觉 费尔德曼教授的研究将与 与这些地区。