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、其与一维实动力学的相互作用（特别是在刚性和重正化理论中）、与三维双曲几何和叶理理论的相互作用，二维复杂和真实动力学的解析和几何方面。动力系统理论研究物理、生物学、工程学等领域中出现的各种系统的演化，以及简化的数学模型那些系统。在过去的 25 年里，人们已经意识到，即使是一维或二维模型也可以表现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。该提案旨在进一步探索这一动力学分支。