Functions of small growth with no unbounded Fatou components

DOI10.1007/s11854-009-0018-zzbMath1185.30021arXiv0801.3610OpenAlexW2058003661MaRDI QIDQ1031817

G. M. Stallard, Philip J. Rippon

Publication date: 2 November 2009

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

Full work available at URL: https://arxiv.org/abs/0801.3610

zbMATH Keywords

entire functionJulia setFatou set

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Entire functions of one complex variable (general theory) (30D20) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (21)

Iterating the minimum modulus: functions of order half, minimal type ⋮ Slow escaping points of quasiregular mappings ⋮ Baker's conjecture and Eremenko's conjecture for functions with negative zeros ⋮ Spiders' webs in the punctured plane ⋮ Fast escaping points of entire functions: a new regularity condition ⋮ Functions with no unbounded Fatou components ⋮ Unbounded fast escaping wandering domains ⋮ A sharp growth condition for a fast escaping spider's web ⋮ Bounded Fatou components of composite transcendental entire functions with gaps ⋮ Slow escape in tracts ⋮ The escaping set of transcendental self-maps of the punctured plane ⋮ Lyapunov exponents and related concepts for entire functions ⋮ Slow escaping points of meromorphic functions ⋮ Maximally and non-maximally fast escaping points of transcendental entire functions ⋮ Escaping points of entire functions of small growth ⋮ The iterated minimum modulus and conjectures of Baker and Eremenko ⋮ Eremenko points and the structure of the escaping set ⋮ Entire functions for which the escaping set is a spider's web ⋮ Growth conditions for entire functions with only bounded Fatou components ⋮ Annular itineraries for entire functions ⋮ Bounded Fatou components of transcendental entire functions with order less than 1/2

Cites Work

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• Growth conditions for entire functions with only bounded Fatou components
• Zusammensetzungen ganzer Funktionen
• Composite entire functions with no unbounded Fatou components
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• On questions of Fatou and Eremenko
• Fatou components of entire functions of small growth
• Unbounded domains of normality
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• On Sets Where Iterates of a Meromorphic Function Zip Towards Infinity
• Unbounded domains of normality of entire functions of small growth
• ON A THEOREM OF BESICOVITCH
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
• Bounded domains of the Fatou set of an entire function
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