Chaotic Dynamics and Fractals - 1st Edition - ISBN: 9780120790609, 9781483269085

Chaotic Dynamics and Fractals

1st Edition

Editors: Michael F. Barnsley Stephen G. Demko
eBook ISBN: 9781483269085
Imprint: Academic Press
Published Date: 28th April 1986
Page Count: 304
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Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry.

This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals.

This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.

Table of Contents



I. Chaos and Fractals

Chaos: Solving the Unsolvable, Predicting the Unpredictable!

Making Chaotic Dynamical Systems to Order

On the Existence and Non-Existence of Natural Boundaries for Non-Integrable Dynamical Systems

The Henon Mapping in the Complex Domain

Dynamical Complexity of Maps of the Interval

A Use of Cellular Automata to Obtain Families of Fractals

II. Julia Sets

Exploding Julia Sets

Algorithms for Computing Angles in the Mandelbrot Set

The Parameter Space for Complex Cubic Polynomials

Disconnected Julia Sets

Calculation of Taylor Series for Julia Sets in Powers of a Parameter

Diophantine Properties of Julia Sets

III. Applications

Real Space Renormalization and Julia Sets in Statistical Mechanics

Regular and Chaotic Cycling in Models from Population and Ecological Genetics

A Bifurcation Gap for a Singularly Perturbed Delay Equation

Travelling Waves for Forced Fisher's Equation


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© Academic Press 1986
Academic Press
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About the Editor

Michael F. Barnsley

Stephen G. Demko

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