Parameter rays in the space of exponential maps

We investigate the setIof parametersκ∈ℂ for which the singular orbit (0,eκ,…) ofEκ(z):=exp (z+κ) converges to$\infty $. These parameters are organized in curves in parameter space calledparameter rays, together with endpoints of certain rays. Parameter rays are an important tool to understand the detailed structure of exponential parameter space. In this paper, we construct and investigate these parameter rays. Based on these results, a complete classification of the setIis given in the following paper [M. Förster, L. Rempe and D. Schleicher. Classification of escaping exponential maps.Proc. Amer. Math. Soc.136(2008), 651–663].