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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
DOI: https://doi.org/10.1090/S0002-9939-02-06494-8
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, 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: https://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

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