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A family of entire functions with Baker domains

Fleischmann, Dominique S. (2009). A family of entire functions with Baker domains. Ergodic Theory and Dynamical Systems, 29(2) pp. 495–514.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1017/S0143385708080383
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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 f(z) = z+(sin?z/?z)+c 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.

Item Type: Journal Article
Copyright Holders: 2008 Cambridge University Press
ISSN: 1469-4417
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 15823
Depositing User: Colin Smith
Date Deposited: 24 Apr 2009 15:25
Last Modified: 24 Oct 2012 04:11
URI: http://oro.open.ac.uk/id/eprint/15823
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