Riemann Surfaces, Dynamics and Hyperbolic Geometry

黎曼曲面、动力学和双曲几何

• 批准号: 9806424
• 负责人: Curtis McMullen
• 金额: $ 43.39万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9806424&HistoricalAwards=false
• 关键词: Riemann; Surfaces; Dynamics; Hyperbolic; Geometry

Riemann Surfaces, Dynamics and Hyperbolic Geometry-C. McMullen DMS-9806424 This project will study the classification of geometric structures and dynamical systems, in settings that allow for a concerted study of specific examples. Its scope includes iterated rational maps, Kleinian groups, projective structures on Riemann surfaces, and algebraic dynamics on the projective plane. Renormalization, the interaction of spectral theory with complex dynamics, and applications of Teichmuller theory to 3-manifolds are among the main research directions. From meteorology to robotics, the control and prediction of dynamical systems plays a central role in science and technology. This project will include computer explorations of mathematically simple systems that exhibit rich combinatorial structure and universal analytic features. Its aim is to advance the theoretical understanding of dynamics and geometry.

黎曼曲面、动力学和双曲几何-C。 McMullen DMS-9806424 该项目将在允许对特定示例进行协调研究的环境中研究几何结构和动力系统的分类。 其范围包括迭代有理图、克莱因群、黎曼曲面上的射影结构以及射影平面上的代数动力学。 重正化、谱理论与复杂动力学的相互作用以及Teichmuller理论在3-流形中的应用是主要研究方向。 从气象学到机器人技术，动力系统的控制和预测在科学技术中发挥着核心作用。 该项目将包括对数学简单系统的计算机探索，这些系统表现出丰富的组合结构和通用分析特征。 其目的是增进对动力学和几何的理论理解。