Chaotic Dynamics and Fractals

Chaotic Dynamics and Fractals

1st Edition - April 28, 1986

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  • Editors: Michael F. Barnsley, Stephen G. Demko
  • eBook ISBN: 9781483269085

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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

  • Contributors


    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

Product details

  • No. of pages: 304
  • Language: English
  • Copyright: © Academic Press 1986
  • Published: April 28, 1986
  • Imprint: Academic Press
  • eBook ISBN: 9781483269085

About the Editors

Michael F. Barnsley

Stephen G. Demko

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