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Basic complex dynamicsA computational approach

Mark McClure

Front Matter

Preface

1 Introduction

Images of complex dynamics
Surprise in Newton's method
Exercises

2 The basics of real iteration

Basic notions
Experimentation
Graphical analysis
The classification of fixed points
Classification of periodic orbits
Parametrized families of functions
A closer look at the bifurcation diagram
The doubling map and chaos
Conjugacy
Tent maps and Cantor sets
A few notes on computation
Exercises

3 The complex quadratic family

An illustrative example
The filled Julia set
An algorithm for the filled Julia set
Another look at conjugacy
The critical orbit
The Mandelbrot set
The components of the Mandelbrot set
Exercises

4 The iteration of complex polynomials

A general escape time algorithm
Critical orbits for polynomials
The cubic bifurcation locus
Exercises

5 Local theory of periodic orbits

Linearization near an attractive fixed point
Linearization near a repelling fixed point
Conjugation near a super-attractive fixed point
Neutral points
Infinity as a super-attractive fixed point
Exercises

Authored in PreTeXt

Section 3.4 Another look at conjugacy

In this section, we'll look at some consequences of conjugacy within the quadratic family.

3.4.1 Representing all quadratics
3.4.2 The chaotic squaring map
3.4.3 A line segment

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