Research in Dynamical Systems

动力系统研究

• 批准号: 0103646
• 负责人: Mikhail Lyubich
• 金额: $ 19.63万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103646&HistoricalAwards=false
• 关键词: Research; Dynamical; Systems

The proposal outlines a program of exploring different aspects of lowdimensional dynamics:combinatorial and geometric issues of holomorphic dynamics,its interplay with one-dimensional real dynamics (particularly in the rigidity and renormalization theories),interaction with three dimensional hyperbolic geometry and the theory offoliations, analytic and geometric aspects of two dimensional complex andreal dynamics.The dynamical systems theory studies the evolution of various systemsarising in physics, biology, engineering etc., as well as simplifiedmathematical models for those systems. It has been realized in the past 25years that even one- or two- dimensional models can exhibit rich andimportant phenomena. It has been also realized that the methods of complexanalysis provide powerful tools for dealing with these systems. Theproposal intends to explore further this branch of dynamics.

该提案概述了探索低维动力学不同方面的计划：全纯动力学的组合和几何问题，它与一维实动力学的相互作用(特别是在刚性和重正化理论方面)，与三维双曲几何的相互作用，以及二维复杂和实动力学的理论，解析和几何方面。动力系统理论研究物理、生物、工程等领域中各种系统的演化，以及这些系统的简化数学模型。在过去的25年里，人们已经认识到，即使是一维或二维的模型也可以显示出丰富而重要的现象。人们还认识到，复杂分析方法为处理这些系统提供了强大的工具。该提案打算进一步探索动力学的这一分支。