Dynamics in One Complex Variable: Introductory Lectures

✍ Scribed by John Milnor (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 2000
• Tongue: English
• Leaves: 264
• Edition: 2
• Category: Library

✦ Synopsis

This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. It is based on introductory lectures given by the author at Stony Brook, NY, in the past ten years.
The subject is large and rapidly growing. These notes are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. The exposition is clear and enriched by many beautiful illustrations.

✦ Table of Contents

Front Matter....Pages i-vii
Riemann Surfaces....Pages 1-37
Iterated Holomorphic Maps....Pages 38-72
Local Fixed Point Theory....Pages 73-131
Periodic Points: Global Theory....Pages 132-147
Structure of the Fatou Set....Pages 148-159
Using the Fatou Set to Study the Julia Set....Pages 160-201
Back Matter....Pages 202-257

✦ Subjects

Engineering, general