Real Submanifolds and Holomorphic Mappings in Several Complex Variables

多个复变量中的实子流形和全纯映射

• 批准号: 0072003
• 负责人: Xianghong Gong
• 金额: $ 7.35万
• 依托单位: Oklahoma State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072003&HistoricalAwards=false
• 关键词: Real; Submanifolds; Holomorphic; Mappings; Several

AbstractAward: DMS-0072003Principal Investigator: Xianghong GongThe long term goal of this project is to study holomorphicmappings and real submanifolds arising in the field of severalcomplex variables. One topic of proposed research is on theexistence of periodic points of reversible and symplecticholomorphic mappings near an elliptic fixed point of general typeand on the integrability property of holomorphic symplecticmappings via meromorphic eigenfunctions. Another topic is on thetopological and analytic structure of singular Levi-flat realhypersurfaces in connections with singular complexhypersurfaces. Other topics include the structure ofnon-reversible conformal mappings and their connections with thenon-reversibility of real analytic Hamiltonian systems.The differential equations dealing with the motion of Nmasspoints (a model of the solar system) in the three-dimensionalspace attracting each other according to Newton's law form aHamiltonian system. The periodic orbits of certainarea-preserving mappings corresponds to the periodic motion inthe Hamiltonian system of the restricted three body problem, andthe study of the existence of such periodic orbits goes back atleast to the work of Poincare and Birkhoff about a centuryago. Holomorphic symplectic mappings are natural extensions ofarea-preserving ones. Such an extension might allow one to applymethods in complex variables to the study of real Hamiltoniansystems. Indeed, recent work on the existence of non-reversiblearea-preserving mappings depends on some deep knowledge ofconformal mappings studied extensively in complex analysis.

AbstractAward：DMS-0072003原理研究者：江冈该项目的长期目标是研究在多个复合变量领域中产生的全态性和真实的子手机。拟议的研究的一个主题是关于通过Meromorphic eigenformintions的全态形态符号符号的一般性固定点附近的椭圆形固定点附近的椭圆形固定点附近的可逆和符号晶状体形态映射的一个主题。另一个主题是关于与奇异的复杂性播放方面的连接中的单数levi-flat Realhypersurfaces的thepologologicy total和分析结构。其他主题包括可逆的保形映射的结构及其与实际分析性汉密尔顿系统的当时可逆性的连接。根据纽顿法律形式的Ahamiltonian System，在三二维标准空间中处理NMASSPoints（太阳系模型）的微分方程（太阳系模型）相互吸引。限制了三个身体问题的哈密顿量系统的周期性运动，对这种周期性轨道的存在的研究与Poincare和Birkhoff的工作大约一个世纪相对应。全体形态符号映射是具有预防物体的自然扩展。这样的扩展可能会使人们可以将复杂变量的方法应用于对真正的哈密顿系统的研究。的确，关于非转换映射的存在的最新工作取决于对复杂分析中广泛研究的对符号映射的一些深刻知识。