Texts and Readings in Mathematics

This volume 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. This subject is large and rapidly growing. These lectures are intended to introduce 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.

Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field. 1. Riemann Surfaces
2.Iterated Holomorphic Maps
3. Local Fixed Point Theory
4. Periodic Points: Global Theory
5. Structure of the Fatou Set
6. Using the Fatou Set to Study the Julia Set
Appendix
References
Index