Mathematical Sciences: Research in Riemann Surfaces and Dynamical Systems

数学科学：黎曼曲面和动力系统研究

• 批准号: 9201321
• 负责人: Howard Masur
• 金额: $ 9.74万
• 依托单位: University of Illinois at Chicago
• 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: 1992-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201321&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Riemann; Surfaces

The principal investigator will use methods from Riemann surface theory to study problems in dynamical systems. In particular, he will use the theory of quadratic differentials and Teichmuller theory to study the ergodic theory of measured folliations, interval exchange transformations, and rational billiards. This award will support research in the general area of dynamical systems. A process which is very simple and easy to understand locally can become extremely complicated, nonlinear, and difficult to analyze globally. Dynamical systems is the study of this local to global relationship. Many physical systems can best be modeled using this area of mathematics including fluid flow and turbulence, complex biological systems, mechanical systems, and chemical reactions.

首席研究员将使用黎曼方法 曲面理论研究动力系统中的问题。在 特别是，他将使用二次微分理论， Teichmuller理论来研究测度的遍历理论 folliations，区间交换变换，和理性 台球。 该奖项将支持一般领域的研究， 动力系统一个非常简单和容易的过程， 局部理解可能会变得极其复杂、非线性， 很难在全球范围内进行分析。动力系统是一项研究 从本地到全球的关系。许多物理系统可以 最好是用这一领域的数学建模，包括流体 流动和湍流，复杂的生物系统，机械 系统和化学反应。