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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the set where the iterates of an entire function are bounded


Author: Walter Bergweiler
Journal: Proc. Amer. Math. Soc. 140 (2012), 847-853
MSC (2010): Primary 37F10, 30D05, 37F35
Published electronically: November 3, 2011
MathSciNet review: 2869069
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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.


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Additional Information

Walter Bergweiler
Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany
Email: bergweiler@math.uni-kiel.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11456-4
PII: S 0002-9939(2011)11456-4
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.