Abstract
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 λn for n from a set with positive density amongst natural numbers.
Funding Statement
Partial support from the Research Training Network CODY is acknowledged.
Citation
Jacek Graczyk. Grzegorz Świa̧tek. "Asymptotic porosity of planar harmonic measure." Ark. Mat. 51 (1) 53 - 69, April 2013. https://doi.org/10.1007/s11512-011-0154-4
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