Mathematical Sciences: The Dynamical Theory of Tilings and Quasicrystals

数学科学：平铺和准晶体的动力学理论

• 批准号: 9007831
• 负责人: E. Arthur Robinson
• 金额: $ 4.41万
• 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: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007831&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Theory; Tilings

Professor Robinson will conduct research in the area of multi-dimensional symbolic dynamical systems associated with tilings of the plane and higher dimensional Euclidean spaces. These dynamical systems are continuous actions of n-dimensional Euclidean space on compact metric spaces. They are related to Ambrose-Kakutani-Rudolph representation theory. In addition, Professor Robinson will continue his work on how various ergodic properties lift to extensions. In particular he will concentrate on how joinings lift to extensions. In the early 1980's experimental physicists were surprised to see five-fold rotational symmetry in what they thought to be a periodic crystal. This is however a mathematical impossibility and it was later observed that the substance was not periodic but rather "quasiperiodic". The research of Professor Robinson will attempt to apply techniques from ergodic theory and dynamical systems to understand this situation.

罗宾逊教授将在以下领域进行研究： 多维符号动力系统 平面和高维欧氏空间的平铺。 这些动力系统是n维的连续作用 紧度量空间上的欧氏空间。 它们涉及 安布罗斯-角谷-鲁道夫表示理论 此外，本发明还提供了一种方法， 罗宾逊教授将继续他的工作如何各种遍历 物业升降机扩展。 尤其是他会集中精力 关于连接如何提升到延伸。 20世纪80年代初，实验物理学家们惊讶地发现， 在他们认为是 周期性晶体 然而这在数学上是不可能的 后来发现这种物质不是周期性的， 而是“准周期性的”。 罗宾逊教授的研究将 尝试应用遍历理论和动力学的技术 系统来了解这种情况。