On the Hausdorff dimension of the escaping set of certain meromorphic functions

DOI10.1090/S0002-9947-2012-05514-0zbMath1294.37018arXiv0901.3014OpenAlexW2006686695WikidataQ115181045 ScholiaQ115181045MaRDI QIDQ2841405

Walter Bergweiler, Janina Kotus

Publication date: 25 July 2013

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

Full work available at URL: https://arxiv.org/abs/0901.3014

zbMATH Keywords

Hausdorff dimensionmeromorphic functionsescaping 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) Dimension theory of smooth dynamical systems (37C45)

Related Items (12)

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 ⋮ Hausdorff measure of escaping sets on certain meromorphic functions ⋮ Hausdorff Dimension of Sets of Escaping Points and Escaping Parameters for Elliptic Functions ⋮ Escaping points and escaping parameters for singly periodic meromorphic maps: Hausdorff dimensions outlook ⋮ Hausdorff dimensions of escaping sets of transcendental entire functions ⋮ Stable components in the parameter plane of transcendental functions of finite type ⋮ Absence of line fields and Mañé’s theorem for nonrecurrent transcendental functions ⋮ Hausdorff dimension of escaping sets of meromorphic functions ⋮ The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class

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