Complex manifolds and algebraic dynamics

复流形和代数动力学

• 批准号: 0245419
• 负责人: Curtis McMullen
• 金额: $ 46.23万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245419&HistoricalAwards=false
• 关键词: Complex; manifolds; algebraic; dynamics

Complex Manifolds and Algebraic Dynamics C. McMullen DMS-0245419 AbstractThis project investigates the behavior ofdynamical systems in settings where the methods of complex analysisand algebraic geometry can be brought to bear.The core of the proposal focuses on three types ofarea-preserving dynamical systems: * Automorphisms of algebraic surfaces, * Polygonal billiards and * Planar fluid flow.Analysis of the rich and still mysterious structure ofthese systems entails many methods, ranging from estimatesfor differential equations with minimal smoothness to rigidity results for Lie groups acting on bundles over the moduli space of Riemann surfaces.From meteorology to robotics, from fluid mechanics toquantum field theory, the control and prediction of dynamical systems plays a central role in science and technology.This project will include computer explorations of mathematically simplesystems that exhibit rich combinatorial structure and universal analytic features. Its aim is to advance the theoretical understanding of dynamics and geometry.

复流形与代数动力学 C. McMullen DMS-0245419摘要该项目研究了在复分析和代数几何方法可以发挥作用的环境中动力系统的行为。该提案的核心集中在三种类型的面积保持动力系统上：* 代数曲面的自同构，* 多边形台球和 * 平面流体流动。分析这些系统的丰富而神秘的结构需要许多方法，从微分方程最小光滑度的估计到李群作用于黎曼曲面模空间上的丛的刚性结果，从气象学到机器人学，从流体力学到量子场论，动力系统的控制和预测在科学和技术中起着中心作用。这个项目将包括对数学上简单的系统进行计算机探索，这些系统表现出丰富的组合结构和普遍性。分析特征。 其目的是推进动力学和几何的理论理解。