Subject Code: MA7L016 Subject Name:  Complex Dynamics L-T-P: 3-1-0 Credit:4
Pre-requisite(s):  Complex Analysis (MA5L007)
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.
Text Books:
  1. Beardon A. F. Iteration of Rational Functions, Springer
  2. Carleson  L. and Gamelin T.W.  Complex Dynamics, Springer
Reference Books:
  1. Milnor J.  Dynamics in one complex variable, Princeton University Press
  2. Morosawa S. Holomorphic Dynamics, Oxford University Press
  3. Shleicher D.  Complex Dynamics-Families and Friends, AK Peters Ltd
  4. Rippon P. J.  and Stallard G. Transcendental Dynamics and Complex Analysis,Cambridge University Press
  5. McMullen C. T. Complex Dynamics and Renormalization, Princeton University Press.