Mathematical Sciences: Symplectic and Poisson Geometry

数学科学：辛几何和泊松几何

• 批准号: 8701318
• 负责人: Hermann Flaschka
• 金额: $ 17.05万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701318&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Poisson; Geometry

This wide-ranging project will involve researchers at both Arizona and Berkeley. The underlying theme of the research is the concept of Hamiltonian system or Poisson structure. The topics to be covered have the potential for significant applications to both mathematics and physics. The investigations will cover the following topics and their interconnections: Poisson geometry and the bundle picture; transverse structures, Lie algebras, and singularities; differential equations in the complex domain; algebraic Poisson structures; geometry of bifurcations and normal forms of Hamiltonian systems; Hamiltonian chaos; modulation theory; Kac- Moody Lie algebras and integrable systems.

这个范围广泛的项目将涉及两个研究人员 亚利桑那和伯克利。研究的基本主题是 哈密顿系统或泊松结构的概念。的议题 具有重要的应用潜力， 数学和物理。 调查将涵盖以下主题及其 互连：泊松几何和束图; 横向结构、李代数和奇点; 复域微分方程;代数泊松 结构;分叉的几何形状和规范形式 哈密顿系统;哈密顿混沌;调制理论; Kac- Moody李代数与可积系统