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A question of Eremenko and Lyubich concerning completely invariant domains and indirect singularities
Author(s):
Walter
Bergweiler
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3231-3236.
MSC (2000):
Primary 37F10;
Secondary 30D05, 30D30
Posted:
May 22, 2002
MathSciNet review:
1913000
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Abstract:
We give an example of an entire function with a completely invariant Fatou component which has an indirect singularity not contained in this Fatou component. The question of whether such a function exists has been raised by Eremenko and Lyubich.
References:
-
- 1.
- I. N. Baker, Completely invariant domains of entire functions, in Mathematical Essays Dedicated to A. J. Macintyre, edited by H. Shankar, Ohio University Press, Athens, Ohio, 1970, 33-35. MR 42:6227
- 2.
- -, The domains of normality of an entire function, Ann. Acad. Sci. Fenn. (Ser. A, I. Math.) 1 (1975), 277-283. MR 53:5867
- 3.
- A. E. Eremenko and M. Yu. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier 42 (1992), 989-1020. MR 93k:30034
- 4.
- R. Nevanlinna, Analytic Functions, Springer, Berlin, Heidelberg, New York, 1970. MR 43:5003
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Additional Information:
Walter
Bergweiler
Affiliation:
Mathematisches Seminar, Christian--Albrechts--Universität zu Kiel, Ludewig--Meyn--Str. 4, D--24098 Kiel, Germany
Email:
bergweiler@math.uni-kiel.de
DOI:
10.1090/S0002-9939-02-06494-8
PII:
S 0002-9939(02)06494-8
Received by editor(s):
March 12, 2001
Posted:
May 22, 2002
Additional Notes:
The author was supported by G.I.F., G -643-117.6/1999 and INTAS-99-00089
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2002,
American Mathematical Society
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