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.

2001年在纽约州立大学石溪分校举行的动力学系统会议是为了纪念约翰·米尔诺（John Milnor），会议强调了与他自己的工作密切相关的动力学领域：单变量和多变量全纯动力学、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论，以及拓扑和生物学中的相关主题。动力系统是根据确定性规律随时间演化的现象的数学模型。这部分数学的某些方面是非常经典的，因为牛顿用来描述重力作用下运动的微分方程导致了一个动力系统。尽管这些模型完全由初始条件和随时间进化的规则决定，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，许多注意力集中在演化规则由一个复变量的多项式函数定义的系统上，以及当多项式系数改变时这些系统的行为。这类系统在某些方面已被发现是依赖于一个参数的动力行为族的行为的普遍模型，但是尽管它们的定义简单，关于全纯动力系统的许多问题仍然是神秘的。