Hausdorff dimension and biaccessibility for polynomial Julia sets
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- by Philipp Meerkamp and Dierk Schleicher PDF
- Proc. Amer. Math. Soc. 141 (2013), 533-542 Request permission
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.References
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Additional Information
- Philipp Meerkamp
- Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
- Email: pmeerkamp@math.cornell.edu
- Dierk Schleicher
- Affiliation: School of Engineering and Science, Jacobs University, Postfach 750 561, D-28725 Bremen, Germany
- MR Author ID: 359328
- Email: dierk@jacobs-university.de
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 533-542
- MSC (2010): Primary 37F10, 37F20, 37F35
- DOI: https://doi.org/10.1090/S0002-9939-2012-11323-1
- MathSciNet review: 2996957