Conference "Around Dynamics"

摘要奖：DMS-0110251首席研究员：Mikhail Lyubi 2001年在纽约州立大学石溪分校举行的关于动力系统的会议是为了纪念John Milnor，并强调了与他自己的工作密切相关的领域：一元和几个变量的全纯动力学，非一致双曲动力学，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是非常经典的，因为牛顿用来描述在重力作用下的运动的微分方程式导致了一个动力系统。尽管这些模型完全由起始条件和随时间演变的规则决定，但详细的预测是困难的，我们必须寻求定性的理解。在过去的二十五年里，人们非常关注由复变量的多项式函数定义其演化规则的系统，以及当多项式的系数改变时，这些系统的行为。这类系统已经被发现在某些方面是依赖于参数的动力学行为族的行为的通用模型，但是尽管它们的定义很简单，关于全纯动力系统的许多事情仍然是神秘的。

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.