Chaos and fractals : the mathematics behind the computer graphics ; [lecture notes prepared for the American Mathematical Society Short Course Chaos and Fractals, the Mathematics Behind the Computer, held in Providence, Rhode Island August 6-7, 1988

This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research. The Terms Chaos And Fractals Have Received Widespread Attention In Recent Years. The Alluring Computer Graphics Images Associated With These Terms Have Heightened Interest Among Scientists In These Ideas. This Volume Contains The Introductory Survey Lectures Delivered In The American Mathematical Society Short Course, Chaos And Fractals: The Mathematics Behind The Computer Graphics, On August 6-7, 1988, Given In Conjunction With The Ams Centennial Meeting In Providence, Rhode Island. In His Overview, Robert L. Devaney Introduces Such Key Topics As Hyperbolicity, The Period Doubling Route To Chaos, Chaotic Dynamics, Symbolic Dynamics And The Horseshoe, And The Appearance Of Fractals As The Chaotic Set For A Dynamical System. Linda Keen And Bodil Branner Discuss The Mandelbrot Set And Julia Sets Associated To The Complex Quadratic Family Z -> Z2 + C. Kathleen T. Alligood, James A. Yorke, And Philip J. Holmes Discuss Some Of These Topics In Higher Dimensional Settings, Including The Smale Horseshoe And Strange Attractors. Jenny Harrison And Michael F. Barnsley Give An Overview Of Fractal Geometry And Its Applications. -- From Dust Jacket. Overview : Dynamics Of Simple Maps / Robert L. Devaney -- Nonlinear Oscillations And The Smale Horseshoe Map / Philip J. Holmes -- Fractal Basin Boundaries And Chaotic Attractors / Kathleen T. Alligood And James A. Yorke -- Julia Sets / Linda Keen -- The Mandelbrot Set / Bodil Branner -- Introduction To Fractals / Jenny Harrison -- Iterated Function Systems / Michael F. Barnsley. Robert L. Devaney And Linda Keen, Editors ; [authors] Kathleen T. Alligood ... [et Al.]. Includes Bibliographical References And Index. "Robert Devaney communicates his deep understanding as well as his enthusiasm for chaos, fractals, and dynamical systems. Starting at a level suitable for well-prepared high school students, he tells the mathematical story behind these fascinating topics. Equations and graphs are clearly shown with computer-generated characters, and Devaney's explanations are lucid and instructive. Illustrating the mathematics are forays into the colorful, unpredictable world of fractals and Julia sets. Devaney explains how the computer is used to generate the pictures and shows how the various colors are chosen for graphical representations ... Though the mathematical background required is elementary, those at the collegiate level and beyond will appreciate ... the clarity of exposition and the sheer beauty of the graphics."--Container