Harmonic Measure Versus Hausdorff Measures on Repellers for Holomorphic Maps

DOI10.2307/2001777zbMath0766.30018OpenAlexW2004005078MaRDI QIDQ3977225

Anna Zdunik

Publication date: 25 June 1992

Full work available at URL: https://doi.org/10.2307/2001777

zbMATH Keywords

harmonic measureHausdorff measuresRiemann map

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Capacity and harmonic measure in the complex plane (30C85) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

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Sublinear measures, Menger curvature, and Hausdorff dimension ⋮ Fine structure of connectedness loci ⋮ Accessibility and porosity of harmonic measure at bifurcation locus ⋮ On Hausdorff dimension of polynomial not totally disconnected Julia sets ⋮ Matrix random products with singular harmonic measure ⋮ Julia set concerning Yang-Lee theorem ⋮ Finer geometric rigidity of limit sets of conformal IFS

Cites Work

• The dimension of the maximal measure for a polynomial map
• Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps. I
• Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map
• Brownian motion and sets of harmonic measure zero
• Parabolic orbifolds and the dimension of the maximal measure for rational maps
• Riemann map and holomorphic dynamics
• On the Distortion of Boundary Sets Under Conformal Mappings
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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