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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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