Hausdorff dimensions of escaping sets of transcendental entire functions

DOI10.1090/S0002-9939-09-10104-1zbMath1201.37075arXiv0904.3072MaRDI QIDQ3558996

G. M. Stallard, Lasse Rempe-Gillen

Publication date: 11 May 2010

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

Full work available at URL: https://arxiv.org/abs/0904.3072

zbMATH Keywords

Julia setHausdorff dimensiontranscendental entire functionescaping 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) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (16)

On the set where the iterates of an entire function are bounded ⋮ The exact value of Hausdorff dimension of escaping sets of class \(\mathcal{B}\) meromorphic functions ⋮ Extended escaping set for meromorphic functions outside a countable set of transcendental singularities ⋮ Hausdorff dimension of escaping sets of meromorphic functions II ⋮ Hausdorff Dimension of Escaping Sets of Nevanlinna Functions ⋮ On the packing dimension of the Julia set and the escaping set of an entire function ⋮ Brushing the hairs of transcendental entire functions ⋮ A generalized family of transcendental functions with one dimensional Julia sets ⋮ Dynamic rays of bounded-type entire 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 ⋮ A new characterisation of the Eremenko-Lyubich class ⋮ On the set where the iterates of an entire function are neither escaping nor bounded ⋮ Lebesgue measure of escaping sets of entire functions of completely regular growth ⋮ Hausdorff dimension of escaping sets of meromorphic functions

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