Dynamics in one complex variable: introductory lectures

TL;DR

This paper provides an introductory overview of the dynamics of iterated holomorphic maps on Riemann surfaces, focusing on rational maps of the Riemann sphere, aimed at newcomers to the field.

Contribution

It offers foundational insights and key ideas in complex dynamics, serving as a basis for further study in the area.

Findings

Introduction to key concepts in complex dynamics

Focus on rational maps of the Riemann sphere

Educational resource for beginners

Abstract

These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. They are based on introductory lectures given at Stony Brook during the Fall Term of 1989-90. These lectures 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.