Conference "Around Dynamics"

“围绕动力学”会议

• 批准号: 0110251
• 负责人: Mikhail Lyubich
• 金额: $ 1.26万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0110251&HistoricalAwards=false
• 关键词: Conference; Around; Dynamics

AbstractAward: DMS-0110251Principal Investigator: Mikhail LyubichThis conference on dynamical systems at SUNY Stony Brook in 2001is held in honor of John Milnor and emphasizes areas of dynamicsclose to his own work: holomorphic dynamics in one and severalvariables, non-uniformly hyperbolic dynamics, fluid dynamics,geometric function theory and thermodynamical formalism, relatedtopics in topology and in biology.Dynamical systems are mathematical models of phenomena thatevolve in time according to deterministic laws. Some aspects ofthis part of mathematics are extremely classical, since thedifferential equations used by Newton to describe motion underthe force of gravity lead to a dynamical system. Although thesemodels are entirely determined by starting conditions and therules for evolution over time, detailed prediction is difficultand we are obliged to seek qualitative understanding. Over thelast twenty-five years much attention has concentrated on systemswhose evolutionary rule is defined by a polynomial function of acomplex variable, and on the behavior of these systems as thepolynomial's coefficients are changed. This class of systems hasbeen found to be a universal model in some ways for the behaviorof families of dynamical behavior depending upon a parameter, butdespite their simplicity of definition much remains mysteriousabout holomorphic dynamical systems.

摘要奖：DMS-0110251 首席研究员：Mikhail Lyubich 2001 年在纽约州立大学石溪分校举行的动力系统会议是为了纪念 John Milnor，并强调与他自己的工作密切相关的动力学领域：一个和多个变量的全纯动力学、非均匀双曲动力学、流体动力学，几何函数理论和热力学形式主义，拓扑学和生物学中的相关主题。动力系统是根据确定性定律随时间演化的现象的数学模型。 这部分数学的某些方面非常经典，因为牛顿用来描述重力下运动的微分方程导致了动力系统。 尽管这些模型完全由起始条件和随时间演化的规则决定，但详细的预测是困难的，我们不得不寻求定性的理解。 在过去的二十五年里，人们的注意力集中在其演化规则由复变量的多项式函数定义的系统上，以及这些系统在多项式系数发生变化时的行为上。 人们发现，这类系统在某些方面是依赖于参数的动态行为族的行为的通用模型，但尽管它们的定义很简单，但全纯动态系统仍然很神秘。