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Parameter rays in the space of exponential maps

Published online by Cambridge University Press:  01 April 2009

MARKUS FÖRSTER  and
DIERK SCHLEICHER
MARKUS FÖRSTER
Affiliation:
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)
DIERK SCHLEICHER
Affiliation:
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)
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Abstract

We investigate the set I of parameters κ∈ℂ for which the singular orbit (0,eκ,…) of Eκ(z):=exp (z+κ) converges to . 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].

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 515 - 544
Copyright
Copyright © Cambridge University Press 2008

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