Iteration of Rational Functions: Complex Analytic Dynamical Systems

Graduate Texts in Mathematics #132

by Alan F. Beardon

This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the proofs have not occurred in print before. The theory of of dynamical systems and chaos has recently undergone a rapid growth in popularity, in part due to the spectacular computer graphics of Julia sets, fractals, and the Mandelbrot set. This text focuses on the specialized area of complex analytic dynamics, a subject that dates back to 1916 and is currently a very active area in mathematics.

Genres: Mathematics

280 pages, Hardcover

First published December 31, 1990

Reviews

[Cheng Jun · Rating 4 out of 5]

Very clear, lucid explanation. Brings the reader through the theory of the iteration of rational functions from simple examples till Sullivan's no-wandering-domains theorem. The exercises are excellent, and the exposition is clear. Proof details are fully worked out for many major theorems in the book, helping the reader.