In this course we will study the dynamics of polynomial and rational maps of the complex plane and Riemann sphere. Although some experience with complex analysis and dynamical systems will be assumed, the complete theory of Julia sets and complex dynamics will be developed from scratch. We will begin with the classical results of Fatou, Julia, and Siegel, and then we will cover as much of the recent material as is possible in a one-semester course. In particular, we will discuss Sullivan's "No wandering domains" theorem, his classification of the Fatou set, Douady and Hubbard's detailed analysis of the quadratic family, and Newton's method as an application of the theory of polynomial-like mappings. We may even make a few pretty pictures.

For more details about the subject matter, see my paper in the Bulletin of the American Mathematical Society, 11(1984) pp.85-141.

Textbook: John Milnor, Dynamics in One Complex Variable, Vieweg, 1999. Available from the AMS web site.

Prerequisites: A little discrete dynamics and a little complex analysis. See me if you have questions about the prerequisities.

Related Courses: MA 573, MA 713, MA 771, and COM FT 351.

Paul Blanchard
Office: 255 MCS
Phone: 353-9555