In the last fifteen years, the Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled "Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets", held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.

Readership

Graduate students and researchers in all areas of pure and applied mathematics.

Reviews

"The book is a useful introduction to a survey of this field of active research. It is illustrated with many beautiful pictures of Julia sets, the Mandelbrot set, and other sets related to the theory."

-- Mathematical Reviews

"This collection of lectures ... contains interesting survey articles on the classical work of Julia and Fatou as well as on the more recent work on the synamics of quadratic and cubic polynomials, on Yoccoz puzzles and tableaux, on the spider algorithm and on the dynamics of entire transcendental functions. Much of the book is accessible to anyone with a background on complex analysis. Several impressive color plates are included."

-- Monatshefte für Mathematik

Table of Contents

• R. L. Devaney -- The complex dynamics of quadratic polynomials
• B. Branner -- Puzzles and para-puzzles of quadratic and cubic polynomials
• L. Keen -- Julia sets of rational maps
• A. Douady -- Does a Julia set depend continuously on the polynomial?
• P. Blanchard -- The dynamics of Newton's method
• J. H. Hubbard and D. Schleicher -- The spider algorithm
• R. L. Devaney -- Complex dynamics and entire functions