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.

该提案概述了一个探索低维动力学不同方面的计划：整体动力学的组合和几何问题，与一维实际动力学相互作用（尤其是在刚性和更新的理论中）的相互作用（尤其是在刚性和更高的理论中），与三个维数的几何学以及三维的多体的相互作用，以及两个维度的开放，分析和分析和测定方面的复杂性和几个不同的方面。物理，生物学，工程等各种系统化的演变，以及这些系统的简化数学模型。在过去的25年中，已经意识到，即使是一维模型也可以表现出丰富而重要的现象。还已经意识到，复杂分析的方法为处理这些系统提供了强大的工具。 Proposal打算进一步探索这一动态分支。