This is a careful, modern presentatin of the foundations of dynamical systems and complex analysis, written with an emphasis on clarity, elegance, and detail. Many of the proofs have not occurred in print before. This text is intended for the graduate level.
Alan F. Beardon
A.F. Beardon
Iteration of Rational Functions
Complex Analytic Dynamical Systems
"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."—ZENTRALBLATT MATH