Complex Dynamics

3.0 credits · Graduate

This course studies the iteration of holomorphic maps in one complex variable, with emphasis on the dynamics of polynomials and rational maps on the Riemann sphere. We will cover Julia and Fatou sets, normal families, local and global behavior of periodic points, polynomial dynamics, puzzle techniques and local connectivity problems, quasiconformal methods, and renormalization. Central results include Sullivan’s no wandering domains theorem, the Douady– Hubbard straightening theorem, Yoccoz’s proof of the Siegel Brjuno theorem, and Thurston’s topological characterization of rational functions. The course will also give a glimpse of the connection between complex dynamics with Teichmuller theory, hyperbolic geometry, and geometric group theory.