The principal investigator will study three problems in the area of dynamical systems. These involve geometric Lorenz attractors for systems of equations derived from mathematical physics, the structure of the standard map for large values of the parameter, and cocycles over an irrational rotation and Schrodinger operators with quasi-periodic coefficients. Dynamical systems is the mathematics of how objects move. The Lorenz system of differential equations describes motion in three dimensions. The principal investigator has proven that a systems similar to the Lorenz system displays chaotic behavior and has a "strange attractor." He will extend the techniques used to find this attractor to a wider class of differential equations.
