Proceedings of the American Mathematical Society

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



Hausdorff dimension and biaccessibility for polynomial Julia sets

Authors: Philipp Meerkamp and Dierk Schleicher
Journal: Proc. Amer. Math. Soc. 141 (2013), 533-542
MSC (2010): Primary 37F10, 37F20, 37F35
Published electronically: June 4, 2012
MathSciNet review: 2996957
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Abstract: We investigate the set of biaccessible points for connected polynomial Julia sets of arbitrary degrees $ d\geq 2$. We prove that the Hausdorff dimension of the set of external angles corresponding to biaccessible points is less than $ 1$, unless the Julia set is an interval. This strengthens theorems of Stanislav Smirnov and Anna Zdunik: they proved that the same set of external angles has zero $ 1$-dimensional measure.

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Additional Information

Philipp Meerkamp
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201

Dierk Schleicher
Affiliation: School of Engineering and Science, Jacobs University, Postfach 750 561, D-28725 Bremen, Germany

Keywords: Julia set, polynomial, biaccessible, Hausdorff dimension
Received by editor(s): April 14, 2011
Received by editor(s) in revised form: June 28, 2011
Published electronically: June 4, 2012
Communicated by: Bryna Kra
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.