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#### Classical Analysis and ODEsmathscidoc:1701.05004

Arkiv for Matematik, 51, (1), 53-69, 2010.9
We study the distribution of harmonic measure on connected Julia sets of unicritical polynomials. Harmonic measure on a full compact set in ℂ is always concentrated on a set which is porous for a positive density of scales. We prove that there is a topologically generic set $\mathcal{A}$ in the boundary of the Mandelbrot set such that for every $c\in \mathcal{A}$ ,$β$>0, and$λ$∈(0,1), the corresponding Julia set is a full compact set with harmonic measure concentrated on a set which is not$β$-porous in scale$λ$^{$n$}for$n$from a set with positive density amongst natural numbers.
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@inproceedings{jacek2010asymptotic,
title={Asymptotic porosity of planar harmonic measure},
author={Jacek Graczyk, and Grzegorz Świa̧tek},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634266163033},
booktitle={Arkiv for Matematik},
volume={51},
number={1},
pages={53-69},
year={2010},
}

Jacek Graczyk, and Grzegorz Świa̧tek. Asymptotic porosity of planar harmonic measure. 2010. Vol. 51. In Arkiv for Matematik. pp.53-69. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634266163033.
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