Complex Dynamics

Normal families, Montel's theorem; Iteration of polynomials and rational maps: The structure of the Fatou set, Sullivan classification of Fatou components, External rays, Properties of the Julia set; Polynomial like mappings; Parameter spaces of rational maps: Mandelbrot set, Holomorphic motion and stability; Renormalisation; Dynamics of transcendental entire and meromorphic functions: Singular points of inverse function, Baker domains and Wandering domains, Maps of bounded type, Escaping points, Omitted values and dynamics; Conformal measure on Julia sets, Dimension of Julia sets; Kleinian groups and Sullivan’s dictionary.