Mathematical Sciences: Problems in Complex Analysis

数学科学：复分析中的问题

• 批准号: 9505149
• 负责人: John Fornaess
• 金额: $ 14.81万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505149&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Complex; Analysis

9505149 Fornaess The proposed research lies in the area of several complex variables. Complex dynamical systems in several variables - this is a new area of research founded by the proposer and his coworkers - will be pursued: iteration of holomorphic maps, holomorphic flows, and holomorphic hulls are among the topics of study in this area. The Cauchy-Riemann operator in singular spaces and the boundary regularity of holomorphic mappings will also be investigated. Complex dynamical systems generalize real dynamical systems arising from autonomous systems of ordinary differential equations. Real dynamical systems are widely used to model natural phenomena including fluid flow, planetary motion, and ecological systems. Complex dynamical systems, which are relatively recent constructs, have already found applications in fractal geometry.

9505149 Fornaess提出的研究是在几个复杂变量的领域。多变量的复杂动力系统——这是由提案人及其同事创立的一个新的研究领域——将被追求：全纯映射的迭代、全纯流和全纯壳是该领域的研究主题之一。研究了奇异空间中的Cauchy-Riemann算子和全纯映射的边界正则性。复动力系统是由常微分方程自治系统产生的实动力系统的推广。真实动力系统被广泛用于模拟自然现象，包括流体流动、行星运动和生态系统。复杂的动力系统，这是相对较新的结构，已经在分形几何中找到了应用。