Boundaries of escaping Fatou components

DOI10.1090/S0002-9939-2011-10842-6zbMath1291.37071arXiv1009.4450OpenAlexW2963815752MaRDI QIDQ3020367

G. M. Stallard, Philip J. Rippon

Publication date: 4 August 2011

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

Full work available at URL: https://arxiv.org/abs/1009.4450

zbMATH Keywords

transcendental entire functionFatou componentescaping setboundary pointsescaping Fatou componentescaping wandering domain

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)

Extended escaping set for meromorphic functions outside a countable set of transcendental singularities ⋮ On topological properties of Fatou sets and Julia sets of transcendental entire functions ⋮ Baker's conjecture and Eremenko's conjecture for functions with negative zeros ⋮ Connectedness properties of the set where the iterates of an entire function are unbounded ⋮ On the connectivity of the escaping set in the punctured plane ⋮ Connectedness properties of the set where the iterates of an entire function are bounded ⋮ Escaping sets are not sigma-compact ⋮ Escaping points in the boundaries of Baker domains ⋮ On the set where the iterates of an entire function are neither escaping nor bounded ⋮ Boundaries of univalent Baker domains ⋮ Dynamical sets whose union with infinity is connected ⋮ Eremenko points and the structure of the escaping set ⋮ On connected preimages of simply-connected domains under entire functions

Cites Work

• An entire function with simply and multiply connected wandering domains
• Escaping points of entire functions of small growth
• Some connectedness properties of julia sets
• Slow escaping points of meromorphic functions
• Entire functions for which the escaping set is a spider's web
• On questions of Fatou and Eremenko
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• On the connectivity of Julia sets of transcendental entire functions
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• Fast escaping points of entire functions
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