A question of Eremenko and Lyubich concerning completely invariant domains and indirect singularities
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- by Walter Bergweiler PDF
- Proc. Amer. Math. Soc. 130 (2002), 3231-3236 Request permission
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
- I. N. Baker, Completely invariant domains of entire functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio, 1970, pp. 33–35. MR 0271344
- I. N. Baker, The domains of normality of an entire function, Ann. Acad. Sci. Fenn. Ser. A I Math. 1 (1975), no. 2, 277–283. MR 0402044
- A. È. Erëmenko and M. Yu. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 4, 989–1020 (English, with English and French summaries). MR 1196102
- Rolf Nevanlinna, Analytic functions, Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. Translated from the second German edition by Phillip Emig. MR 0279280
Additional Information
- Walter Bergweiler
- Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany
- MR Author ID: 35350
- Email: bergweiler@math.uni-kiel.de
- Received by editor(s): March 12, 2001
- Published electronically: 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 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3231-3236
- MSC (2000): Primary 37F10; Secondary 30D05, 30D30
- DOI: https://doi.org/10.1090/S0002-9939-02-06494-8
- MathSciNet review: 1913000