MATH 6280 - Complex Dynamical Systems

Spring. 4 credits.

Prerequisite: MATH 4180. Not offered every year.

Staff.

Various topics in the dynamics of analytic mappings in one complex variable, such as: Julia and Fatou sets, the Mandelbrot set, Mañé-Sad-Sullivan’s theorem on structural stability. Also covers: local theory, including repulsive cycles and the Yoccoz inequality, parabolic points and Ecalle-Voronin invariants, Siegel disks and Yoccoz’s proof of the Siegel Brjuno theorem; quasi-conformal mappings and surgery: Sullivan’s theorem on non-wandering domains, polynomial-like mappings and renormalization, Shishikura’s construction of Hermann rings; puzzles, tableaux and local connectivity problems; and Thurston’s topological characterization of rational functions, the spider algorithm, and mating of polynomials.