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.
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