Introduction

This introductory chapter is an overview into holomorphic dynamics—one of the earliest branches of dynamical systems which is not part of classical mechanics. Holomorphic dynamics studies iterates of holomorphic maps on complex manifolds. As a prominent field in its own right, holomorphic dynamics was founded early in the twentieth century, but was almost completely forgotten for sixty years, only to be revived in the early 1980s partly due to the efforts of John Milnor. The field of holomorphic dynamics is rich in interactions with many branches of mathematics; such as complex analysis, geometry, topology, number theory, algebraic geometry, combinatorics, and measure theory. This chapter briefly explores the extent of such interplay.