Mathematical Sciences: Topics in Dynamical Systems and Smooth Ergodic Theory

数学科学：动力系统和平滑遍历理论主题

• 批准号: 9011749
• 负责人: Anatole Katok
• 金额: $ 3.37万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-01 至 1991-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9011749&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Dynamical; Systems

The principal investigator will analyze interrelated problems concerning hyperbolic dynamical systems and compact Riemannian manifolds of negative curvature. Specifically, he will investigate the classification, differentiability, and regularity of stable and unstable foliations. Other directions of research include investigations of rigidity and regularity of global invariants with respect to external parameters. This project involves three areas of mathematical research. Dynamical systems is the study of where points go after many repeated iterations of a continuous function. Ergodic theorists ask where most, but not all, points go under many such iterations. And Riemannian geometry is concerned with the curvature and other aspects of the base space from which these points are taken. The principal investigator will analyze several problems which stem from attempts to apply theories from all three of these areas at once.

主要研究人员将分析有关双曲动力系统和紧致负曲率黎曼流形的相关问题。具体地说，他将研究稳定和不稳定叶的分类、可微性和规律性。其他研究方向包括关于外部参数的全局不变量的刚性和正则性的研究。这个项目涉及三个领域的数学研究。动力系统是研究在连续函数的多次重复迭代后点的去向的学科。遍历理论家问，在许多这样的迭代下，大多数但不是所有的点都在哪里。黎曼几何关注的是这些点所在的基本空间的曲率和其他方面。首席研究员将分析几个问题，这些问题源于试图同时应用这三个领域的理论。