Boundaries of escaping Fatou components
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- by P. J. Rippon and G. M. Stallard PDF
- Proc. Amer. Math. Soc. 139 (2011), 2807-2820 Request permission
Abstract:
Let $f$ be a transcendental entire function and $U$ be a Fatou component of $f$. We show that if $U$ is an escaping wandering domain of $f$, then most boundary points of $U$ (in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of $U$ are escaping, then $U$ is an escaping Fatou component. Some applications of these results are given; for example, if $I(f)$ is the escaping set of $f$, then $I(f)\cup \{\infty \}$ is connected.References
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Additional Information
- P. J. Rippon
- Affiliation: Department of Mathematics and Statistics, 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 Mathematics and Statistics, 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): July 23, 2010
- Published electronically: March 2, 2011
- Additional Notes: Both authors were supported by EPSRC grant EP/H006591/1.
- Communicated by: Mario Bonk
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2807-2820
- MSC (2010): Primary 37F10; Secondary 30D05
- DOI: https://doi.org/10.1090/S0002-9939-2011-10842-6
- MathSciNet review: 2801622