Iteration of Rational Functions: Complex Analytic Dynamical Systems

Graduate Texts in Mathematics #132

by Alan F. Beardon

This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.

Genres: Mathematics

296 pages, Paperback

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.