Are Devaney hairs fast escaping?

DOI10.1080/10236190903282824zbMath1201.30027arXiv0904.1403OpenAlexW3103470674WikidataQ56005138 ScholiaQ56005138MaRDI QIDQ3570141

G. M. Stallard, Philip J. Rippon, Lasse Rempe-Gillen

Publication date: 24 June 2010

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.1403

zbMATH Keywords

iterationfast escaping settranscendental entire functionsDevaney hairs

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)

Related Items (14)

Dynamics of generalised exponential maps ⋮ Non-escaping endpoints do not explode ⋮ Totally disconnected Julia set for different classes of meromorphic functions ⋮ On topological properties of Fatou sets and Julia sets of transcendental entire functions ⋮ On the dimension of points which escape to infinity at given rate under exponential iteration ⋮ ON THE ITERATIONS AND THE ARGUMENT DISTRIBUTION OF MEROMORPHIC FUNCTIONS ⋮ Escape rate and Hausdorff measure for entire functions ⋮ A landing theorem for entire functions with bounded post-singular sets ⋮ Dynamic rays of bounded-type transcendental self-maps of the punctured plane ⋮ Slow escaping points of meromorphic functions ⋮ Speiser class Julia sets with dimension near one ⋮ Dynamics in the Eremenko-Lyubich class ⋮ Eremenko points and the structure of the escaping set ⋮ Combinatorics of criniferous entire maps with escaping critical values

Cites Work

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• On questions of Fatou and Eremenko
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• Dynamics of meromorphic functions with direct or logarithmic singularities
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• Dynamics of entire functions near the essential singularity
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• ESCAPING POINTS OF EXPONENTIAL MAPS
• The Hausdorff Dimension of Julia Sets of Entire Functions IV
• Coding trees and boundaries of attracting basins for some entire maps
• Topological dynamics of exponential maps on their escaping sets

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