## On questions of Fatou and Eremenko

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**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.## References

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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
- 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

Dedicated: This paper is dedicated to the memory of Professor Noel Baker