The principal investigators will conduct research in various aspects of dynamical systems. The investigators will concentrate primarily on low dimensional systems. In particular they will study attractors for unimodal maps of the interval, determination of asymptotic properties of the renormalization operator, and the problem of topological exponential maps. They will also consider iterations of homeomorphisms of the annulus and the dynamics of flows on three manifolds. This award will support research in the general area of dynamical systems. A process which is very simple and easy to understand locally can become extremely complicated, nonlinear, and difficult to analyze globally. Dynamical systems is the study of this local to global relationship. Many physical systems can best be modeled using this area of mathematics including fluid flow and turbulence, complex biological systems, mechanical systems, and chemical reactions.
