Entire functions for which the escaping set is a spider's web

DOI10.1017/S0305004111000582zbMath1238.37014arXiv1012.1303OpenAlexW3100911815MaRDI QIDQ3095784

David J. Sixsmith

Publication date: 4 November 2011

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

Full work available at URL: https://arxiv.org/abs/1012.1303

zbMATH Keywords

spider's webfast escaping setiteration of transcendental entire functions

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 (16)

Extended escaping set for meromorphic functions outside a countable set of transcendental singularities ⋮ Unnamed Item ⋮ Slow escaping points of quasiregular mappings ⋮ On topological properties of Fatou sets and Julia sets of transcendental entire functions ⋮ Spiders' webs in the punctured plane ⋮ Fast escaping points of entire functions: a new regularity condition ⋮ 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 ⋮ Maximum term of transcendental entire function and spider’s web ⋮ Boundaries of escaping Fatou components ⋮ 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 ⋮ Hollow quasi-Fatou components of quasiregular maps ⋮ On slow escaping and non-escaping points of quasimeromorphic mappings ⋮ Dynamical sets whose union with infinity is connected ⋮ Fatou’s web

Cites Work

• Unnamed Item
• Functions of small growth with no unbounded Fatou components
• Boundedness of Fatou components of holomorphic maps
• Zusammensetzungen ganzer Funktionen
• On the coefficients of an entire series
• Composite entire functions with no unbounded Fatou components
• The Local Growth of Power Series: A Survey of the Wiman-Valiron Method
• Unbounded domains of normality
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• Exponential Numbers
• Angular Value Distribution of Power Series with Gaps
• On the Fatou set of an entire function with gaps

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