On the Hausdorff dimension of the Julia set of a regularly growing entire function

DOI10.1017/S0305004109990491zbMath1198.30027arXiv0909.3988WikidataQ122583769 ScholiaQ122583769MaRDI QIDQ3559983

Walter Bergweiler, Bogusława Karpińska

Publication date: 17 May 2010

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3988

zbMATH Keywords

Julia setdensityHausdorff dimensionescaping set

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items

Wiman–Valiron Discs and the Dimension of Julia Sets ⋮ On the packing dimension of the Julia set and the escaping set of an entire function ⋮ Fast escaping points of entire functions: a new regularity condition ⋮ A generalized family of transcendental functions with one dimensional Julia sets ⋮ ON THE ITERATIONS AND THE ARGUMENT DISTRIBUTION OF MEROMORPHIC FUNCTIONS ⋮ Escape rate and Hausdorff measure for entire functions ⋮ Dimensions of slowly escaping sets and annular itineraries for exponential functions ⋮ Escaping points and escaping parameters for singly periodic meromorphic maps: Hausdorff dimensions outlook ⋮ Entire functions with Julia sets of positive measure ⋮ Fast growth entire functions whose escaping set has Hausdorff dimension two ⋮ Cantor bouquets in spiders’ webs ⋮ Lebesgue measure of escaping sets of entire functions of completely regular growth ⋮ Functions of genus zero for which the fast escaping set has Hausdorff dimension two

Cites Work

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• Dynamical properties of some classes of entire functions
• Comparisons between T(r,f) and the total variation of \(\arg f(re^{i\theta})\) and \(\log | f(re^{i\theta})|\)
• Linear combinations of logarithmic derivatives of entire functions with applications to differential equations
• On multiply-connected Fatou components in iteration of meromorphic functions
• Hausdorff dimension of hairs and ends for entire maps of finite order
• The growth rate of an entire function and the Hausdorff dimension of its Julia set
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• Iteration of meromorphic functions
• Size of the Julia set of a structurally finite transcendental entire function
• The Hausdorff dimension of Julia sets of entire functions II
• On the Characteristic of Functions Meromorphic in the Plane and of their Integrals
• Inequalities for the Logarithmic Derivatives of a Polynomial

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