Mathematical Sciences: Deformations of Complex Structures

数学科学：复杂结构的变形

• 批准号: 9204092
• 负责人: Irwin Kra
• 金额: $ 37.73万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204092&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Deformations; Complex; Structures; Mathematical; Sciences; Deformations; Complex; Structures

The principal investigators will study dynamical systems in the classical case of the complex plane. One investigator will study the relationship between harmonic measure and analytic capacity. The other two investigators will continue their research on the moduli spaces associated with Kleinian groups and Teichmuller theory. The research spans classical analysis in one complex variable, group theory, and differential geometry. 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.

主要研究人员将在复杂平面的经典案例中研究动态系统。一个研究者将研究谐波测量和分析能力之间的关系。另外两个研究人员将继续研究与克莱恩群体和蒂奇穆勒理论相关的模量空间。该研究跨越经典分析，以一个复杂的变量，群体理论和差异几何形状。 该奖项将支持动态系统一般领域的研究。一个非常简单易于理解的过程可能会变得非常复杂，非线性且难以分析全球。动力学系统是对全球关系的研究。许多物理系统最好使用该数学领域进行建模，包括流体流和湍流，复杂的生物系统，机械系统和化学反应。