A Survey of Exponential Dynamics

In this paper we describe some of the interesting dynamics, topology, and geometry that arises in the iteration of the complex exponential E (z) = e where > 0. There are two quite distinct cases. When 1=e, the Julia set for E is a Cantor bouquet. When > 1=e, the Julia set suddenly explodes and fills the entire plane. We show that it is the appearance of indecomposable continua in the Julia set that accounts for this explosion