Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the Hausdorff dimension of Julia sets of some real polynomials

Authors: Genadi Levin and Michel Zinsmeister
Journal: Proc. Amer. Math. Soc. 141 (2013), 3565-3572
MSC (2010): Primary 37F10
Published electronically: July 1, 2013
MathSciNet review: 3080178
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Abstract: We show that the supremum for $ c$ real of the Hausdorff dimension of the Julia set of the polynomial $ z\mapsto z^d+c$ ($ d$ is an even natural number) is greater than $ 2d/(d+1)$.

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Additional Information

Genadi Levin
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904, Israel

Michel Zinsmeister
Affiliation: MAPMO, Université d’Orléans, BP 6759, 45067 Orléans Cedex 2, France

Received by editor(s): November 23, 2010
Received by editor(s) in revised form: October 18, 2011, and January 4, 2012
Published electronically: July 1, 2013
Additional Notes: The authors were supported in part by the IMPAN-BC European Community Centre of Excellence and by the Marie Curie European network CODY
Communicated by: Mario Bonk
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.