On the set where the iterates of an entire function are bounded
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Abstract:
We show that for a transcendental entire function the set of points whose orbit under iteration is bounded can have arbitrarily small positive Hausdorff dimension.References
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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): December 6, 2010
- Published electronically: November 3, 2011
- Additional Notes: The author was supported by a Chinese Academy of Sciences Visiting Professorship for Senior International Scientists, Grant No. 2010 TIJ10. He was also supported by the Deutsche Forschungsgemeinschaft, Be 1508/7-1, the EU Research Training Network CODY and the ESF Networking Programme HCAA
- 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. 140 (2012), 847-853
- MSC (2010): Primary 37F10, 30D05, 37F35
- DOI: https://doi.org/10.1090/S0002-9939-2011-11456-4
- MathSciNet review: 2869069