Hölder exponents of the Green functions of planar polynomial Julia sets

DOI10.1007/s10231-012-0278-6zbMath1300.30049OpenAlexW2092297973WikidataQ122705562 ScholiaQ122705562MaRDI QIDQ2014994

Marta Kosek

Publication date: 18 June 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-012-0278-6

zbMATH Keywords

iterationJulia setspolynomialsHölder continuitycomplex Green function

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (3)

Complete invariance and compactness of the filled Julia sets of polynomial maps in \( \mathbb {C}^N \) ⋮ Orthogonal polynomials on generalized Julia sets ⋮ Hölder exponents for the pluricomplex Green function of Julia type sets

Cites Work

• Hölder exponents of Green's functions of Cantor sets
• Complex dynamics
• On the best exponent in Markov inequality
• Invariant sets under iteration of rational functions
• A remark on the shape of quadratic Julia sets
• Markov's Exponent of Compact Sets in ℂ n
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