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

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.

主要研究人员将研究动力系统， 复平面的经典例子。一名调查员将 研究调和测度与解析测度的关系 容量另外两名调查人员将继续他们的 与Kleinian群相关的模空间的研究， Teichmuller理论这项研究将经典分析融为一体， 复变量、群论和微分几何。 该奖项将支持一般领域的研究， 动力系统一个非常简单且易于操作的过程 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。