On questions of Fatou and Eremenko

DOI10.1090/S0002-9939-04-07805-0zbMath1058.37033OpenAlexW1701808593MaRDI QIDQ3155943

G. M. Stallard, Philip J. Rippon

Publication date: 5 January 2005

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-04-07805-0

zbMATH Keywords

Julia settranscendental entire functionFatou setno bounded components

Mathematics Subject Classification ID

Related Items (45)

The dynamics of semigroups of transcendental entire functions. II ⋮ Iteration of quasiregular tangent functions in three dimensions ⋮ A transcendental Julia set of dimension 1 ⋮ Unnamed Item ⋮ Trees and hairs for some hyperbolic entire maps of finite order ⋮ Non-escaping endpoints do not explode ⋮ Slow escaping points of quasiregular mappings ⋮ On topological properties of Fatou sets and Julia sets of transcendental entire functions ⋮ Permutable quasiregular maps ⋮ Baker's conjecture and Eremenko's conjecture for functions with negative zeros ⋮ Iteration of quasiregular mappings ⋮ Permutable entire functions and multiply connected wandering domains ⋮ Fast escaping points of entire functions: a new regularity condition ⋮ 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 ⋮ Dynamic rays of bounded-type entire functions ⋮ Escape rate and Hausdorff measure for entire functions ⋮ The fast escaping set for quasiregular mappings ⋮ Slow escape in tracts ⋮ Connectedness properties of the set where the iterates of an entire function are unbounded ⋮ Siegel disks and periodic rays of entire functions ⋮ Entire functions with Julia sets of positive measure ⋮ The escaping set of the exponential ⋮ The escaping set of transcendental self-maps of the punctured plane ⋮ Dynamic rays of bounded-type transcendental self-maps of the punctured plane ⋮ Slow escaping points of meromorphic functions ⋮ Boundaries of escaping Fatou components ⋮ Are Devaney hairs fast escaping? ⋮ Escaping sets are not sigma-compact ⋮ The Julia set and the fast escaping set of a quasiregular mapping ⋮ On the set where the iterates of an entire function are neither escaping nor bounded ⋮ Maximally and non-maximally fast escaping points of transcendental entire functions ⋮ The escaping set of a quasiregular mapping ⋮ Escaping points of entire functions of small growth ⋮ The iterated minimum modulus and conjectures of Baker and Eremenko ⋮ The dynamics of quasiregular maps of punctured space ⋮ Fatou’s web ⋮ Functions of small growth with no unbounded Fatou components ⋮ Lebesgue measure of escaping sets of entire functions of completely regular growth ⋮ Poincaré functions with spiders’ webs ⋮ Functions of genus zero for which the fast escaping set has Hausdorff dimension two ⋮ Unnamed Item ⋮ Escaping points of meromorphic functions with a finite number of poles

Cites Work

• Wandering Domains in the Iteration of Entire Functions
• Dynamics of entire functions near the essential singularity
• On the connectivity of Julia sets of transcendental entire functions
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• ESCAPING POINTS OF EXPONENTIAL MAPS
• On Sets Where Iterates of a Meromorphic Function Zip Towards Infinity
• Invariant domains and singularities
• Unnamed Item
• Unnamed Item

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