Iteration of Rational Functions: Complex Analytic Dynamical Systems

Paperback | September 27, 2000

byAlan F. Beardon

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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.

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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 imp...

Format:PaperbackDimensions:296 pages, 9.25 × 6.1 × 0.04 inPublished:September 27, 2000Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387951512

ISBN - 13:9780387951515

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Table of Contents

Examples.- Rational Maps.- The Fatou and Julia Sets.- Properties of the Julia Set.- The Structure of the Fatou Set.- Periodic Points.- Forward Invariant Components.- The No Wandering Domains Theorem.- Critical Points.- Hausdorff Dimension.- Examples.- References.

Editorial Reviews

A.F. BeardonIteration of Rational FunctionsComplex 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