Harmonic measure and polynomial Julia sets

DOI10.1215/S0012-7094-03-11725-1zbMath1036.30017OpenAlexW2043866337WikidataQ101118435 ScholiaQ101118435MaRDI QIDQ1394591

Ilia A. Binder, Nikolai Makarov, Stanislav Smirnov

Publication date: 2003

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-03-11725-1

zbMATH Keywords

Julia setHausdorff dimensionharmonic measureconformal Cantor set

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Capacity and harmonic measure in the complex plane (30C85)

Related Items

Fine structure of connectedness loci, Dimension of the harmonic measure of non-homogeneous Cantor sets, Sensitive dependence of geometric Gibbs states at positive temperature, Analytic structures and harmonic measure at bifurcation locus, High-order phase transitions in the quadratic family, Accessibility and porosity of harmonic measure at bifurcation locus, Nice inducing schemes and the thermodynamics of rational maps, Low-temperature phase transitions in the quadratic family, Thermodynamic formalism and integral means spectrum of logarithmic tracts for transcendental entire functions, Fekete polynomials and shapes of Julia sets, Geometric pressure for multimodal maps of the interval

Cites Work

• The dimension of the maximal measure for a polynomial map
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• Hausdorff dimension of harmonic measures in the plane
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• Complex dynamics
• Area distortion of quasiconformal mappings
• On the Distortion of Boundary Sets Under Conformal Mappings
• On a theorem of Fatou
• Harmonic measure and expansion on the boundary of the connectedness locus.
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