Complex dynamics with illustrations using mathematica.

• Other Authors: Ip, Che-ho.
• Format: Others
• Language: English
• Published: 1997
• Subjects: Functions of complex variables; Fixed point theory
• Online Access: http://library.cuhk.edu.hk/record=b5889314; http://repository.lib.cuhk.edu.hk/en/item/cuhk-321980

by Ip Che-ho. === Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. === Includes bibliographical references (leaf 136). === Covering Page --- p.i === Acknowledgement --- p.ii === Abstract --- p.iii === Table of Content --- p.v === Chapter 1. --- Fundamentals of Complex Analys --- p.is === Chapter 1.1 --- The extended complex plane --- p.1 === Chapter 1.2 --- Stereographic projection --- p.2 === Chapter 1.3 --- Analytic functions --- p.3 === Chapter 1.4 --- Rational functions --- p.5 === Chapter 1.5 --- Mobius transformation --- p.6 === Chapter 2. --- The Topology of the Extended Plane === Chapter 2.1 --- The topology of S2 and C ∞ --- p.9 === Chapter 2.2 --- Smooth map and manifolds --- p.10 === Chapter 2.3 --- Regular points --- p.11 === Chapter 2.4 --- Degree of maps --- p.13 === Chapter 2.5 --- Euler characteristics --- p.14 === Chapter 2.6 --- Covering space --- p.16 === Chapter 2.7 --- Riemann-Hurwritz formula --- p.17 === Chapter 3 --- The Montel Theorem === Chapter 3.1 --- Introduction --- p.21 === Chapter 3.2 --- Normality and Equicontinuous --- p.21 === Chapter 3.3 --- Local boundedness --- p.23 === Chapter 3.4 --- Covering and uniformization --- p.26 === Chapter 3.5 --- Montel's theorem --- p.28 === Chapter 4 --- Fatou Set and Julia Set === Chapter 4.1 --- Iteration of functions --- p.31 === Chapter 4.2 --- Fatou set and Julia set --- p.35 === Chapter 4.3 --- Iteration of Mobius transformtion --- p.39 === Chapter 4.4 --- Fixed points and their classification --- p.44 === Chapter 4.5 --- Periodic points and cycles --- p.45 === Chapter 4.6 --- Critical points --- p.47 === Chapter 4.7 --- Dlustractions of local behaviour of map near periodic points --- p.48 === Chapter 5 --- More about Julia Set === Chapter 5.1 --- Some examples of Julia set --- p.57 === Chapter 5.2 --- Completely invariant set --- p.58 === Chapter 5.3 --- Exceptional set --- p.61 === Chapter 5.4 --- Properties of Julia set --- p.63 === Chapter 5.5 --- Forward and backward convergence of sets --- p.66 === Chapter 6 --- More about Fatou Set === Chapter 6.1 --- Components of Fatou set --- p.97 === Chapter 6.2 --- Simply connected Fatou components --- p.98 === Chapter 6.3 --- Number of components in Fatou set --- p.100 === Chapter 6.4 --- Classification of forward invariant components of the Fatou set --- p.102 === Chapter 6.5 --- Examples illustrating the five possible forward invariant components --- p.104 === Chapter 7 --- Critical Points === Chapter 7.1 --- Introduction --- p.108 === Chapter 7.2 --- Some interesting results --- p.110 === Chapter 7.3 --- The Fatou set of polynomials --- p.114 === Chapter 7.4 --- Quadratic polynomial and Mandelbrot set --- p.116 === Appendix --- p.125 === Reference --- p.136