ABSTRACT
Our point of departure in this survey is the question “What is there in complex analytic dynamics that would be of interest to continuum theorists?” We will present a collection of results and questions arising in the discrete dynamics of complex analytic maps of the complex plane C and the Riemann sphere C∞. Our focus will be on the topological structure of the Julia sets of entire functions on the complex plane, and the tools used to study this structure. As it happens, there are a number of interesting open topological problems concerning Julia sets. The difficulty appears to be identifying those problems whose solutions are likely to be obtainable by topological methods.
