Fractal Concepts in Nonlinear Dynamics

This chapter contains sections titled: Introduction Koch Curve Cantor Set The Devil's Staircase Fractal Dimension Measures of Fractal Dimension Pointwise Dimension Correlation Dimension Information Dimension Relation Between Dimension Definitions and Lyapunov Exponents How Useful Is Fractal Dimension for Vibration Problems? Fractal Dimension of Strange Attractors Discretization of Phase Space Variables Fractal Dimension of Poincaré Maps Dimension Calculation from Single Time Series Measurement Optical Measurement of Fractal Dimension An Optical Parallel Processor for the Correlation Function Fractal Basin Boundaries Basins of Attraction Sensitivity to Initial Conditions: Transient Motion in a Two-Well Potential Fractal Basin Boundary: Forced Motion in a Two-Well Potential Homo clinic Orbits: A Criterion for Fractal Basin Boundaries Dimension of Basin Boundaries and Uncertainty Transient Decay Times: Sensitivity to Initial Conditions Other Applications Fractal Boundaries for Chaos in Parameter Space Complex Maps and the Mandelbrot Set