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A question of Eremenko and Lyubich concerning completely invariant domains and indirect singularities


Author: Walter Bergweiler
Journal: Proc. Amer. Math. Soc. 130 (2002), 3231-3236
MSC (2000): Primary 37F10; Secondary 30D05, 30D30
Published electronically: 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 [Enhancements On Off] (What's this?)

  • 1. 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
  • 2. 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
  • 3. 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
  • 4. Rolf Nevanlinna, Analytic functions, Translated from the second German edition by Phillip Emig. Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. MR 0279280

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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: http://dx.doi.org/10.1090/S0002-9939-02-06494-8
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
Article copyright: © Copyright 2002 American Mathematical Society