Combinatorics of Bifurcations in Exponential Parameter Space

Abstract

We give a complete combinatorial description of the bifurcation structure in the space of exponential maps $z\mapsto\exp(z)+\kappa$. This combinatorial structure is the basis for a number of important results about exponential parameter space. These include the fact that every hyperbolic component has connected boundary, a classification of escaping parameters, and the fact that all dynamic and parameter rays at periodic addresses land.