Conference "Around Dynamics"

Abstract Award: DMS-0110251 Principal Investigator: Mikhail Lyubich This conference on dynamical systems at SUNY Stony Brook in 2001 is held in honor of John Milnor and emphasizes areas of dynamics close to his own work: holomorphic dynamics in one and several variables, non-uniformly hyperbolic dynamics, fluid dynamics, geometric function theory and thermodynamical formalism, related topics in topology and in biology. Dynamical systems are mathematical models of phenomena that evolve in time according to deterministic laws. Some aspects of this part of mathematics are extremely classical, since the differential equations used by Newton to describe motion under the force of gravity lead to a dynamical system. Although these models are entirely determined by starting conditions and the rules for evolution over time, detailed prediction is difficult and we are obliged to seek qualitative understanding. Over the last twenty-five years much attention has concentrated on systems whose evolutionary rule is defined by a polynomial function of a complex variable, and on the behavior of these systems as the polynomial's coefficients are changed. This class of systems has been found to be a universal model in some ways for the behavior of families of dynamical behavior depending upon a parameter, but despite their simplicity of definition much remains mysterious about holomorphic dynamical systems.