Encounters with Chaos and Fractals

Periodic Points. One-Dimensional Chaos. Two-Dimensional Chaos. Systems of Differential Equations. Introduction to Fractals. Creating Fractals Sets. Complex Fractals: Julia Sets and the Mandelbrot Set. Computer Programs. Answers to Selected Exercises. References. Index.

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• Geometria
• Teoria dos números
• Cálculo diferencial e equações

Space Filling Curve;Negative Schwarzian Derivative;Periodic Points;One-Dimensional Chaos;Fixed Point;Introduction to Fractals;Cantor Ternary Set;Systems of Differential Equations;Mandelbrot Set;Creating Fractals Sets;Tent Function;Cauchy Sequence;Baker's Function;Cantor Set;Julia Set;Asymptotically Stable;Pendulum System;Affine Function;Bifurcation Diagram;Koch Curve;Hausdorff Metric;Self-similar Set;Lorenz System;Menger Sponge;Lyapunov Dimension;Complete Metric Space;Period Doubling Bifurcations;Tangent Bifurcation;Capacity Dimension