Hausdorff dimension and biaccessibility for polynomial Julia sets

Meerkamp, Philipp; Schleicher, Dierk

doi:10.1090/S0002-9939-2012-11323-1

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.

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