Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets
About this Title
Robert L. Devaney, Boston University, Editor
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year: 1994; Volume 49
ISBNs: 978-0-8218-0290-8 (print); 978-0-8218-9264-0 (online)
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.
Graduate students and researchers in all areas of pure and applied mathematics.
Table of Contents
- Robert L. Devaney – The complex dynamics of quadratic polynomials [MR 1315532]
- Bodil Branner – Puzzles and para-puzzles of quadratic and cubic polynomials [MR 1315533]
- Linda Keen – Julia sets of rational maps [MR 1315534]
- Adrien Douady – Does a Julia set depend continuously on the polynomial? [MR 1315535]
- Paul Blanchard – The dynamics of Newton’s method [MR 1315536]
- John H. Hubbard and Dierk Schleicher – The spider algorithm [MR 1315537]
- Robert L. Devaney – Complex dynamics and entire functions [MR 1315538]