The principal investigator will study the dynamics of polynomials of C^2, quadratic differentials, and iteration schemes used in numerical analysis. In doing so he will exploit two analogies. The first of these is the similarities between the dynamical behavior of polynomial diffeomorphisms of C^2 and that of maps of C. The second of these is the similarities between these same polynomials and Axiom A diffeomorphism. In recent years exquisite fractals have been generated by computer iteration of polynomial and rational maps of the complex plane. Of course, each of these were functions of a single complex variable. The principal investigator will extend this theory to include iteration of functions of two complex variables.
