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Chaos and FractalsA computational approach

Mark McClure

Front Matter

Preface

1Introduction

Surprise in Newton's method
The scope of chaos
Exercises

2The iteration of real functions

Basic notions
Graphical analysis
The classification of fixed points
Classification of periodic orbits
Parametrized families of functions
Conjugacy
The doubling map and chaos
Symbolic dynamics
Period three implies chaos
The role of the critical orbit
A closer look at the bifurcation diagram
A few notes on computation
Exercises

Authored in PreTeXt

Section2.10The role of the critical orbit