We use Beurling estimates and Zdunik's theorem to prove that the support of a lamination of the circle corresponding to a connected polynomial Julia set has zero length, unless f is conjugate to a Chebyshev polynomial. Equivalently, except for the Chebyshev case, the biaccessible points in the connected polynomial Julia set have zero harmonic measure.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-11,
author = {Stanislav K. Smirnov},
title = {On supports of dynamical laminations and biaccessible points in polynomial Julia sets},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {287-295},
zbl = {1116.37309},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-11}
}
Stanislav K. Smirnov. On supports of dynamical laminations and biaccessible points in polynomial Julia sets. Colloquium Mathematicae, Tome 89 (2001) pp. 287-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-11/