Mathematical Sciences: The Dynamical Theory of Tilings and Multi-dimensional Symbolic Dynamics

数学科学：平铺动力学理论和多维符号动力学

• 批准号: 9303498
• 负责人: E. Arthur Robinson
• 金额: $ 5.99万
• 依托单位: George Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303498&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Theory; Tilings

Robinson will continue his study of a periodic tilings of Euclidean space. The approach is to view sets of tilings as compact metric spaces, and to study the dynamics of R^n acting on such spaces by translation. In this context, many standard dynamical properties correspond to important properties of tilings. 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.

罗宾逊将继续研究欧几里得空间的周期性平铺。 该方法是将平铺集视为紧度量空间，并通过平移研究 R^n 作用于此类空间的动态。 在这种情况下，许多标准动力学属性对应于平铺的重要属性。 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，遍历理论在寻求对同质空间上的流进行分类的过程中与几何学建立了联系。