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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Introduction

Introduction

Chapter:
(p.1) Introduction
Source:
Frontiers in Complex Dynamics
Author(s):
Araceli Bonifant, Mikhail Lyubich, Scott Sutherland, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0001

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.

Keywords:   holomorphic dynamics, John Milnor, dynamical systems, holomorphic maps, complex manifolds, mathematics, holomorphic dynamics studies

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