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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
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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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