Mathematical Sciences: Ergodic Theory and Dynamics over Teichmuller Space

数学科学：Teichmuller 空间的遍历理论和动力学

• 批准号: 9503542
• 负责人: William Veech
• 金额: $ 10.5万
• 依托单位: William Marsh Rice University
• 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 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503542&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Ergodic; Theory; Dynamics

9503542 Veech The proposed research lies in the area of complex dynamical systems. The proposer wants to evaluate certain integrals over the Teichmuller moduli space coming from an identification of the Teichmuller space with the space of cone metrics. Techniques for the study of the billiard in a regular polygon are expected to play an important role. The Teichmuller moduli space corresponds to a family of pretzel-like surfaces known as compact Riemann surfaces (of a fixed genus); these surfaces play an important role in studying complex-valued functions. The proposed research aims to give a geometric description of some of these surfaces.

小行星9503542 拟议的研究领域在于复杂的动力系统。提议者希望评估Teichmuller模空间上的某些积分，这些积分来自Teichmuller空间与锥度量空间的标识。技术的研究台球在一个正多边形预计将发挥重要作用。 Teichmuller模空间对应于一类类似椒盐卷饼的曲面，称为紧致黎曼曲面（固定亏格）;这些曲面在研究复值函数中起着重要作用。拟议的研究的目的是给一些这些表面的几何描述。