Harmonic measure and expansion on the boundary of the connectedness locus.

DOI10.1007/s002220000100zbMath1052.37041OpenAlexW1990440748MaRDI QIDQ5926385

Grzegorz Świątek, Jacek Graczyk

Publication date: 4 March 2002

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002220000100

zbMATH Keywords

Collet-Eckmann conditioncomplex polynomialsexpansiveness for mapsJulia sets

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50)

Related Items (17)

Statistical properties of topological Collet–Eckmann maps ⋮ Sublinear measures, Menger curvature, and Hausdorff dimension ⋮ Fine structure of connectedness loci ⋮ Analytic structures and harmonic measure at bifurcation locus ⋮ Harmonic measure and polynomial Julia sets ⋮ A characterization of hyperbolic potentials of rational maps ⋮ Geometric methods in holomorphic dynamics ⋮ Accessibility and porosity of harmonic measure at bifurcation locus ⋮ Slowly recurrent Collet–Eckmann maps with non‐empty Fatou set ⋮ Asymptotic porosity of planar harmonic measure ⋮ Asymptotically conformal similarity between Julia and Mandelbrot sets ⋮ Hausdorff dimension of Julia sets in the logistic family ⋮ Distribution of postcritically finite polynomials III: Combinatorial continuity ⋮ Large deviation principles for non-uniformly hyperbolic rational maps ⋮ On the left side derivative of the Hausdorff dimension of the Julia sets for \({z^2+c}\) at \({c=-3/4}\) ⋮ Non-uniform hyperbolicity in complex dynamics ⋮ Parametric Lyapunov exponents

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