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

Authors
Bergweiler, W Eremenko, A
Citation
W. Bergweiler et A. Eremenko, Entire functions of slow growth whose Julia set coincides with the plane, ERGOD TH DY, 20, 2000, pp. 1577-1582
Citations number
18
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
20
Year of publication
2000
Part
6
Pages
1577 - 1582
Database
ISI
SICI code
0143-3857(200012)20:<1577:EFOSGW>2.0.ZU;2-B
Abstract
We construct a transcendental entire function f with J(f) = C such that f h as arbitrarily slow growth; that is, log \f(z)\ less than or equal to phi(\ z\) log \z\ for \z\ > r(0), where phi is an arbitrary prescribed function t ending to infinity.