RESEARCH IN DYNAMICAL SYSTEMS

Abstract DMS-0401266 PI: John W. Milnor CoPI: Mikhail Lyubich, Saeed Zakeri Since its founding in 1989, the Institute for Mathematical Sciences at Stony Brook has carried on an active program of research and education in dynamical systems, and related areas of geometry, ergodic theory, and complex analysis, with particular emphasis on low dimensional dynamics over the real and complex numbers. It has supported a number of junior and senior visitors, organized nine conferences, worked with graduate and undergraduate students, and helped promote communication in this field by maintaining a dynamics web site and an active preprint series. The present proposal outlines a further program of exploring all aspects of low dimensional dynamics: combinatorial and geometric issues of holomorphic dynamics, its interplay with one-dimensional real dynamics (particularly in the rigidity and renormalization theories), interaction with three-dimensional hyperbolic geometry, analytic and geometric aspects of two dimensional complex and real dynamics.