Dynamics in one complex variable : introductory lectures

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. 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 Riemann Surfaces -- Iterated Holomorphic Maps -- Local Fixed Point Theory -- Periodic Point : Global Theory -- Structure Of The Fatou Set -- Using The Fatou Set To Study The Julia Set. John Milnor. Includes Bibliographical References (p. 246-255) And Index.