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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Classification of escaping exponential maps


Authors: Markus Förster, Lasse Rempe and Dierk Schleicher
Journal: Proc. Amer. Math. Soc. 136 (2008), 651-663
MSC (2000): Primary 37F10; Secondary 30D05
Published electronically: November 1, 2007
MathSciNet review: 2358507
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Abstract: We give a complete classification of the set of parameters $ \kappa$ for which the singular value of $ E_{\kappa}:z\mapsto \exp(z)+\kappa$ escapes to $ \infty$ under iteration. In particular, we show that every path-connected component of this set is a curve to infinity.


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Additional Information

Markus Förster
Affiliation: KPMG Deutsche Treuhand-Gesellschaft, Marie-Curie-Straße 30, 60439 Frankfurt/ Main, Germany
Email: mfoerster@kpmg.com

Lasse Rempe
Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom
Email: l.rempe@liverpool.ac.uk

Dierk Schleicher
Affiliation: International University Bremen, P.O. Box 750 561, 28725 Bremen, Germany
Email: dierk@iu-bremen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09073-9
PII: S 0002-9939(07)09073-9
Received by editor(s): September 1, 2005
Received by editor(s) in revised form: January 16, 2007
Published electronically: November 1, 2007
Additional Notes: The first author was supported in part by a European fellowship of the Marie Curie Fellowship Association.
The second author was supported in part by a postdoctoral fellowship of the German Academic Exchange Service (DAAD) and by the German-Israeli Foundation for Scientific Research and Development (G.I.F.), grant no.\ G-643-117.6/1999
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society