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| A Mathematical and Historical Tour | |
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| Images from Dynamical Systems | |
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| A Brief History of Dynamics | |
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| Examples of Dynamical Systems | |
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| An Example from Finance | |
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| An Example from Ecology | |
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| Finding Roots and Solving Equations | |
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| Differential Equations | |
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| Orbits | |
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| Iteration | |
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| Orbits | |
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| Types of Orbits | |
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| Other Orbits | |
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| The Doubling Function | |
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| Experiment: The Computer May Lie | |
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| Graphical Analysis | |
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| Graphical Analysis | |
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| Orbit Analysis | |
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| The Phase Portrait | |
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| Fixed and Periodic Points | |
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| A Fixed Point Theorem | |
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| Attraction and Repulsion | |
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| Calculus of Fixed Points | |
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| Why Is This True? | |
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| Periodic Points | |
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| Experiment: Rates of Convergence | |
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| Bifurcations | |
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| Dynamics of the Quadratic Map | |
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| The Saddle-Node Bifurcation | |
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| The Period-Doubling Bifurcation | |
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| Experiment: The Transition to Chaos | |
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| The Quadratic Family | |
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| The Case c = -2 | |
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| The Case c [actual symbol not reproducible] -2 | |
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| The Cantor Middle-Thirds Set | |
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| Transition to Chaos | |
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| The Orbit Diagram | |
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| The Period-Doubling Route to Chaos | |
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| Experiment: Windows in the Orbit Diagram | |
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| Symbolic Dynamics | |
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| Itineraries | |
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| The Sequence Space | |
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| The Shift Map | |
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| Conjugacy | |
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| Chaos | |
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| Three Properties of a Chaotic System | |
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| Other Chaotic Systems | |
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| Manifestations of Chaos | |
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| Experiment: Feigenbaum's Constant | |
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| Sarkovskii's Theorem | |
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| Period 3 Implies Chaos | |
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| Sarkovskii's Theorem | |
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| The Period 3 Window | |
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| Subshifts of Finite Type | |
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| The Role of the Critical Orbit | |
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| The Schwarzian Derivative | |
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| The Critical Point and Basins of Attraction | |
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| Newton's Method | |
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| Basic Properties | |
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| Convergence and Nonconvergence | |
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| Fractals | |
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| The Chaos Game | |
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| The Cantor Set Revisited | |
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| The Sierpinski Triangle | |
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| The Koch Snowflake | |
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| Topological Dimension | |
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| Fractal Dimension | |
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| Iterated Function Systems | |
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| Experiment: Iterated Function Systems | |
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| Complex Functions | |
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| Complex Arithmetic | |
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| Complex Square Roots | |
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| Linear Complex Functions | |
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| Calculus of Complex Functions | |
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| The Julia Set | |
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| The Squaring Function | |
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| The Chaotic Quadratic Function | |
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| Cantor Sets Again | |
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| Computing the Filled Julia Set | |
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| Experiment: Filled Julia Sets and Critical Orbits | |
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| The Julia Set as a Repellor | |
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| The Mandelbrot Set | |
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| The Fundamental Dichotomy | |
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| The Mandelbrot Set | |
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| Experiment: Periods of Other Bulbs | |
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| Experiment: Periods of the Decorations | |
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| Experiment: Find the Julia Set | |
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| Experiment: Spokes and Antennae | |
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| Experiment: Similarity of the Mandelbrot and Julia Sets | |
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| Further Projects and Experiments | |
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| The Tricorn | |
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| Cubics | |
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| Exponential Functions | |
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| Trigonometric Functions | |
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| Complex Newton's Method | |
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| Appendix A. Mathematical Preliminaries | |
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| Appendix B. Algorithms | |
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| Appendix C. References | |
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| Index | |