Conference "Around Dynamics"

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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.