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:
- Beardon A. F. Iteration of Rational Functions, Springer
- Carleson L. and Gamelin T.W. Complex Dynamics, Springer
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Reference Books:
- Milnor J. Dynamics in one complex variable, Princeton University Press
- Morosawa S. Holomorphic Dynamics, Oxford University Press
- Shleicher D. Complex Dynamics-Families and Friends, AK Peters Ltd
- Rippon P. J. and Stallard G. Transcendental Dynamics and Complex Analysis,Cambridge University Press
- McMullen C. T. Complex Dynamics and Renormalization, Princeton University Press.
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