Mathematical Sciences: Joinings, Combinatorics and Ergodic Theory

数学科学：连接、组合学和遍历理论

• 批准号: 9112595
• 负责人: Jonathan King
• 金额: --
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9112595&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Joinings; Combinatorics; Ergodic

Professor King will study a number of questions in ergodic theory. He will consider potential generalizations of a structure theorem based on joinings. He will investigate the "continuous selection problem", related to work of Oxtoby and Ulam. He will study two combinatorial problems: the 2-fold 3- fold mixing problem and the van den Berg-Kesten "box conjecture". 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.

金教授将研究遍历理论中的一些问题。 他将考虑基于连接的结构定理的潜在推广。 他将研究与奥克斯托比和乌拉姆的工作相关的“连续选择问题”。 他将研究两个组合问题：2重3重混合问题和van den Berg-Kest​​en“盒子猜想”。 该项目涉及遍历理论的研究。 一般来说，遍历理论涉及理解系统的平均行为，这些系统的动力学过于复杂或混乱，无法在微观细节中遵循。 在“动力学”标题下可以放置关于抽象变换组如何作用于平滑空间的现代理论。 通过这种方式，遍历理论与几何学相联系，寻求对均匀空间上的流进行分类。