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Basic complex dynamics
A computational approach
Mark McClure
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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
The critical orbit
The Mandelbrot set
The components of the Mandelbrot set
Exercises
Authored in PreTeXt
Basic complex dynamics
A computational approach
Mark McClure
Department of Mathematics
University of North Carolina at Asheville
mcmcclur@unca.edu
February 4, 2019
Preface
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