Parameter rays for the exponential family

Research paper by Markus Förster, Dierk Schleicher

Indexed on: 06 May '05Published on: 06 May '05Published in: Mathematics - Dynamical Systems

Abstract

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}.