Parameter rays for the exponential family

Markus Förster, Dierk Schleicher

Published 2005-05-06Version 1

We investigate the set of parameters $\kappa\in\C$ for which the singular orbit $(0,e^{\kappa},...)$ of $E_{\kappa}(z):=\exp(z+\kappa)$ converges to $\infty$. These parameters are organized in smooth curves in parameter space called \emph{parameter rays}.