Research in Dynamical Systems

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

The proposal outlines a program of exploring different 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 and the theory of foliations, analytic and geometric aspects of two dimensional complex and real dynamics. The dynamical systems theory studies the evolution of various systems arising in physics, biology, engineering etc., as well as simplified mathematical models for those systems. It has been realized in the past 25 years that even one- or two- dimensional models can exhibit rich and important phenomena. It has been also realized that the methods of complex analysis provide powerful tools for dealing with these systems. The proposal intends to explore further this branch of dynamics.