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A family of entire functions with Baker domains

Published online by Cambridge University Press:  01 April 2009

DOMINIQUE S. FLEISCHMANN
DOMINIQUE S. FLEISCHMANN*
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK (email: splasher2001@hotmail.com)
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Abstract

In his paper [The iteration of polynomials and transcendental entire functions. J. Aust. Math. Soc. (Series A)30 (1981), 483–495], Baker proved that the function f defined by has a Baker domain for c sufficiently large. In this paper we use a novel method to prove that f has a Baker domain for all c>0. We also prove that there exists an open unbounded set contained in the Baker domain on which the orbits of points under f are asymptotically horizontal.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 495 - 514
Copyright
Copyright © Cambridge University Press 2008

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References

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