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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_321980 |
| Date | January 1997 |
| Contributors | Ip, Che-ho., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, vi, 136 leaves : ill. (some col.) ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
Page generated in 0.0014 seconds