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Bifurcation in complex quadratic polynomial and some folk theorems involving the geometry of bulbs of the mandelbrot set

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Bifurcation in complex quadratic polynomial and some folk theorems involving the geometry of bulbs of the mandelbrot set

Begum, Monzu Ara (2001) Bifurcation in complex quadratic polynomial and some folk theorems involving the geometry of bulbs of the mandelbrot set. Masters thesis, Concordia University.

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Abstract

The Mandelbrot set M is a subset of the parameter plane for iteration of the complex quadratic polynomial Q c ( z ) = z 2 + c . M consists of those c values for which the orbit of 0 is bounded. This set features a basic cardioid shape from which hang numerous 'bulbs' or 'decorations'. Each of these bulbs is a large disk that is directly attached to the main cardioid together with numerous other smaller bulbs and a prominent 'antenna'. In this thesis we study the geometry of bulbs and some 'folk theorems' about the geometry of bulbs involving spokes of the antenna.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Begum, Monzu Ara
Pagination:vi, 62 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Mathematics and Statistics
Date:2001
Thesis Supervisor(s):Gora, Pawel
ID Code:1443
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:19
Last Modified:08 Dec 2010 10:20
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