Mathematical Sciences: "Dynamics, Hyperbolic Geometry and Quasiconformal Maps"

数学科学：“动力学、双曲几何和拟共形映射”

• 批准号: 9016023
• 负责人: Curtis McMullen
• 金额: $ 8.18万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9016023&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; Hyperbolic; Geometry

The principal investigator will analyze how topology determines geometry in several settings. He will study deformation theory for open 3-manifolds, geometrization of automorphisms of free groups, and parallels between renormalization theory and hyperbolic 3-manifolds which asymptotically fiber over a circle. A central theme in modern dynamical systems is the restriction topology puts on allowable dynamics and geometry. For example, on the surface of a sphere, every vector field must have a singularity. On the earth, this means that the wind cannot blow everywhere at once; there must be at least one spot where the air does not move. In this vein, the principal investigator will develop relationships between complex dynamics and the geometry of three-dimensional hypersurfaces.

首席研究员将分析拓扑如何在多种设置中确定几何形状。 他将研究开 3 流形的变形理论、自由群自同构的几何化，以及重整化理论与在圆上渐近纤维化的双曲 3 流形之间的相似性。 现代动力系统的一个中心主题是拓扑对允许的动力学和几何形状的限制。 例如，在球体表面上，每个矢量场都必须有一个奇点。 在地球上，这意味着风不可能一下子吹到各处；必须至少有一处空气不流动。 在这种情况下，首席研究员将开发复杂动力学与三维超曲面几何之间的关系。