Preface

The concepts of chaos and fractal have become quite popular in recent years, even among people with little mathematical background. Among the reasons for this surge of interest are the publication of several books and articles intended for general audiences. These include James Gleick's Chaos: Making a New Science and articles in Scientific American showing the great beauty of the computer graphics images of complex dynamical systems. At times, all the attention devoted to these topics seems to obscure the fact that there really is some beautiful mathematics in the fields of chaotic dynamical systems and fractal geometry. The goal of the Short Course at which these lectures were given was to remedy this.

The course was called Chaos and Fractals: The Mathematics Behind the Computer Graphics and was organized at the Centennial Meeting of the American Mathematical Society held in Providence, RI, on August 6-7, 1988. The lectures covered a wide range of topics from dynamical systems and fractal geometry. Among many other concepts, the lectures covered the period doubling route to chaos, Smale's horseshoe and symbolic dynamics, strange attractors and their basin boundaries, Julia sets and the Mandelbrot set, Hausdorff and entropy dimension, and applications in engineering and data compression. This book contains expanded versions of the seven lectures delivered during the Short Course.

We would especially like to thank Jim Maxwell, Monica Foulkes, and their staffs from the American Mathematical Society, who coordinated the Short Course. With over 550 participants, this course was the largest in AMS history. Despite the memorable 100o temperatures during the course, we were very pleased with the results.

Robert L. Devaney
Linda Keen

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