Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A landing theorem for periodic rays of exponential maps


Author: Lasse Rempe
Journal: Proc. Amer. Math. Soc. 134 (2006), 2639-2648
MSC (2000): Primary 37F10; Secondary 30D05
Published electronically: March 22, 2006
MathSciNet review: 2213743
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Abstract | References | Similar Articles | Additional Information

Abstract: For the family of exponential maps $ z\mapsto \exp(z)+\kappa$, we show the following analog of a theorem of Douady and Hubbard concerning polynomials. Suppose that $ g$ is a periodic dynamic ray of an exponential map with nonescaping singular value. Then $ g$ lands at a repelling or parabolic periodic point. We also show that there are periodic dynamic rays landing at all periodic points of such an exponential map, with the exception of at most one periodic orbit.


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Additional Information

Lasse Rempe
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Address at time of publication: Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, United Kingdom
Email: lasse@maths.warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08287-6
Received by editor(s): July 30, 2003
Received by editor(s) in revised form: March 30, 2005
Published electronically: March 22, 2006
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.