Baker's conjecture and Eremenko's conjecture for functions with negative zeros

DOI10.1007/s11854-013-0021-2zbMath1283.37049arXiv1112.5103OpenAlexW2078278003WikidataQ123007174 ScholiaQ123007174MaRDI QIDQ393420

Philip J. Rippon, G. M. Stallard

Publication date: 17 January 2014

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.5103

zbMATH Keywords

Julia setFatou setescaping setBaker's conjectureEremenko's conjecturespider's webwinding of image curves

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (13)

On topological properties of Fatou sets and Julia sets of transcendental entire functions ⋮ Permutable entire functions and multiply connected wandering domains ⋮ Spiders' webs in the punctured plane ⋮ Interpolation of power mappings ⋮ Unbounded fast escaping wandering domains ⋮ A generalized family of transcendental functions with one dimensional Julia sets ⋮ A sharp growth condition for a fast escaping spider's web ⋮ On the level of \(Q_{\epsilon} (f)\) in quite fast escaping set and spider's web ⋮ Maximally and non-maximally fast escaping points of transcendental entire functions ⋮ The iterated minimum modulus and conjectures of Baker and Eremenko ⋮ Fatou’s web ⋮ Functions of genus zero for which the fast escaping set has Hausdorff dimension two ⋮ Unnamed Item

Cites Work

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• Dynamic rays of bounded-type entire functions
• Functions of small growth with no unbounded Fatou components
• Growth conditions for entire functions with only bounded Fatou components
• Rational iteration: complex analytic dynamical systems
• A sharp growth condition for a fast escaping spider's web
• Zusammensetzungen ganzer Funktionen
• Boundaries of escaping Fatou components
• On questions of Fatou and Eremenko
• On a question of Eremenko concerning escaping components of entire functions
• On the connectivity of Julia sets of transcendental entire functions
• Iteration of meromorphic functions
• Fast escaping points of entire functions
• Unbounded domains of normality of entire functions of small growth
• ON A THEOREM OF BESICOVITCH

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