Hausdorff dimension and biaccessibility for polynomial Julia sets

Philipp Meerkamp, Dierk Schleicher

Published 2011-01-25, updated 2011-06-28Version 2

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.