Dynamics of Transcendental Entire Functions

Abstract

The theory of complex dynamics, is specifically the iteration of entire mappings, has developed considerably since the work of Fatou and Julia. Although most of the traditional complex dynamics are centered on polynomials and rational maps, transcendental entire functions have rich, often counter intuitive, dynamics stemming from their singularities at infinity. This article provides an overview of fundamental breakthroughs, compiles new developments, and outlines outstanding issues in the dynamics of transcendental entire functions.