In this course, we will first cover the basic theory as developed by P. Fatou and G. Julia early this century.  Then we will prove some of the highlights of the field such as Siegel's theorem (about irrational rotations, we will develop the small amount of number theory necessary) and Sullivan's "`no wandering domains theorem'' (this will need the theory of quasiconformal maps, developed in Math 532A in Winter.)

If time allows, we will also discuss some ergodic theory and "fractal dimensions'' of rational maps and their associated Julia sets.

Textbook: We will largely follow the book of L. Carleson and T. Gamelin, Complex Dynamics.

Prerequisites: Complex Analysis (at least Math 534,535; the uniformization theorem as sometimes proved in Math 536 will be used without proof). The second half of this course could be viewed as a continuation of Math 532A (Geometric Function Theory, Winter 2001), but those willing to take some results from 532 on faith should not have problems following along.