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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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On questions of Fatou and Eremenko
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by P. J. Rippon and G. M. Stallard PDF
Proc. Amer. Math. Soc. 133 (2005), 1119-1126 Request permission

Abstract:

Let $f$ be a transcendental entire function and let $I(f)$ be the set of points whose iterates under $f$ tend to infinity. We show that $I(f)$ has at least one unbounded component. In the case that $f$ has a Baker wandering domain, we show that $I(f)$ is a connected unbounded set.
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Additional Information
  • P. J. Rippon
  • Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
  • MR Author ID: 190595
  • Email: p.j.rippon@open.ac.uk
  • G. M. Stallard
  • Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
  • MR Author ID: 292621
  • Email: g.m.stallard@open.ac.uk
  • Received by editor(s): April 4, 2003
  • Received by editor(s) in revised form: November 28, 2003
  • Published electronically: October 18, 2004

  • Dedicated: This paper is dedicated to the memory of Professor Noel Baker
  • Communicated by: Michael Handel
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1119-1126
  • MSC (2000): Primary 37F10; Secondary 37F45
  • DOI: https://doi.org/10.1090/S0002-9939-04-07805-0
  • MathSciNet review: 2117213