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Unbounded domains of normality
Author(s):
J.
M.
Anderson;
A.
Hinkkanen
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3243-3252.
MSC (1991):
Primary 30D05, 58F23
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Abstract:
Let  be a transcendental entire function of order less than 1/2. We introduce the method of ``self-sustaining spread'' to study the components of the set of normality of such a function. We give a new proof of the fact that any preperiodic or periodic component of the set of normality of  is bounded. We obtain the same conclusion for a wandering domain if the growth rate of  is never too small.
References:
- 1.
- I. N. Baker, Zusammensetzungen ganzer Funktionen, Math. Z. 69 (1958), 121-163. MR 20:4000
- 2.
- -, Fixpoints and iterates of entire functions, Math. Z. 71 (1959), 146-153. MR 21:5743
- 3.
- -, The iteration of polynomials and transcendental entire functions, J. Austral. Math. Soc. (Series A) 30 (1981), 483-495. MR 82g:30043
- 4.
- -, Wandering domains in the iteration of entire functions, Proc. London Math. Soc. (Series 3) 49 (1984), 563-576. MR 86d:58066
- 5.
- P. D. Barry, On a theorem of Besicovitch, Quart. J. Math. Oxford (Series 2) 14 (1963), 292-302. MR 28:234
- 6.
- A. F. Beardon, Iteration of rational functions, Springer, New York, 1991. MR 92j:30026
- 7.
- W. Bergweiler, The iteration of meromorphic functions, Bull. Amer. Math. Soc. 29 (1993), 151-188.
- 8.
- P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France 47 (1919), 161-271.
- 9.
- -, Sur les équations fonctionnelles, Bull. Soc. Math. France 48 (1920), 33-94, 208-314.
- 10.
- -, Sur l'itération des fonctions transcendantes entières, Acta Math. 47 (1926), 337-370.
- 11.
- G. Julia, Mémoire sur l'itération des fonctions rationnelles, J. Math. Pures Appl. 8 (1918), 47-245.
- 12.
- G. Stallard, Some problems in the iteration of meromorphic functions, Ph.D. thesis, Imperial College, London, 1991.
- 13.
- -, The iteration of entire functions of small growth, Math. Proc. Camb. Phil. Soc. 114 (1993), 43-55. MR 95a:30023
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Additional Information:
J.
M.
Anderson
Affiliation:
Department of Mathematics, University College, London WC1E 6BT, United Kingdom
A.
Hinkkanen
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
DOI:
10.1090/S0002-9939-98-04370-6
PII:
S 0002-9939(98)04370-6
Received by editor(s):
July 8, 1996
Received by editor(s) in revised form:
March 10, 1997
Additional Notes:
This research was completed while the first author was visiting the University of Illinois at Urbana-Champaign. He wishes to thank the Department of Mathematics for its kind hospitality.
The research of the second author was partially supported by the Alfred P. Sloan Foundation, by the U.S. National Science Foundation grant DMS 94-00999, and by the U.S. National Security Agency grant MDA904-95-H-1014.
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1998,
American Mathematical Society
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