Hausdorff Dimension of Sets of Escaping Points and Escaping Parameters for Elliptic Functions

DOI10.1017/S0013091515000280zbMath1376.37092WikidataQ115181044 ScholiaQ115181044MaRDI QIDQ2976221

Piotr Galązka, Janina Kotus

Publication date: 28 April 2017

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

zbMATH Keywords

Hausdorff dimensionelliptic functionescaping setescaping parameter

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 (2)

The exact value of Hausdorff dimension of escaping sets of class \(\mathcal{B}\) meromorphic functions ⋮ Hausdorff dimension of escaping sets of meromorphic functions

Cites Work

• Escaping points of meromorphic functions with a finite number of poles
• Ergodic properties and Julia sets of Weierstrass elliptic functions
• On the packing dimension of the Julia set and the escaping set of an entire function
• Geometry and ergodic theory on non-recurrent elliptic functions
• Connectivity properties of Julia sets of Weierstrass elliptic functions
• On the Hausdorff dimension of the escaping set of certain meromorphic functions
• Hausdorff dimension of hairs and ends for entire maps of finite order
• Hausdorff dimension of theM-set of λ exp(z)
• HAUSDORFF DIMENSION AND HAUSDORFF MEASURES OF JULIA SETS OF ELLIPTIC FUNCTIONS
• Fast escaping points of entire functions
• On the Hausdorff dimension of Julia sets of meromorphic functions. II

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