Ergodic Theory and Dynamical Systems

Research Article

Parameter rays in the space of exponential maps

MARKUS FÖRSTERa1 and DIERK SCHLEICHERa1

a1 School of Engineering and Science, Research I, Jacobs University, Formerly International University Bremen, Postfach 750 561, D-28725 Bremen, Germany (email: mfoerster@kpmg.com, dierk@jacobs-university.de)

Abstract

We investigate the set I of parameters κxs2208xs2102 for which the singular orbit (0,eκ,…) of Eκ(z):=exp (z+κ) converges to $\infty $. These parameters are organized in curves in parameter space called parameter 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 set I is 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].

(Received May 10 2005)

(Revised April 08 2008)

Footnotes

Dedicated to Armin Leutbecher on the occasion of his 75th birthday