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Entire functions of slow growth whose Julia set coincides with the plane

Published online by Cambridge University Press:  01 December 2000

WALTER BERGWEILER  and
ALEXANDRE EREMENKO
WALTER BERGWEILER
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany (e-mail: bergweiler@math.uni-kiel.de)
ALEXANDRE EREMENKO
Affiliation:
Purdue University, West Lafayette IN 47907, USA (e-mail: eremenko@math.purdue.edu)
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Abstract

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We construct a transcendental entire function $f$ with $J(f)=\mathbb{C}$ such that $f$ has arbitrarily slow growth; that is, $\log |f(z)|\leq\phi(|z|)\log |z|$ for $|z|>r_0$, where $\phi$ is an arbitrary prescribed function tending to infinity.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 6 , December 2000 , pp. 1577 - 1582
Copyright
© 2000 Cambridge University Press