Exotic Baker and wandering domains for Ahlfors islands maps

DOI10.1007/s11854-012-0023-5zbMath1285.37013arXiv1008.1724OpenAlexW2006431684MaRDI QIDQ351340

Philip J. Rippon, Lasse Rempe-Gillen

Publication date: 11 July 2013

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

Full work available at URL: https://arxiv.org/abs/1008.1724

zbMATH Keywords

Julia setFatou setwandering domainAhlfors five islands theoremBaker domain

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 (8)

Fatou's associates ⋮ Extended escaping set for meromorphic functions outside a countable set of transcendental singularities ⋮ Absence of wandering domains for some real entire functions with bounded singular sets ⋮ Escaping sets are not sigma-compact ⋮ Residual Julia set for functions with the Ahlfors' Property ⋮ On the set where the iterates of an entire function are neither escaping nor bounded ⋮ Hyperbolic dimension and radial Julia sets of transcendental functions ⋮ Constructing entire functions by quasiconformal folding

Cites Work

• Unnamed Item
• Uniform approximation by functions analytic on a Riemann surface
• A new proof of the Ahlfors five islands theorem
• Slow escaping points of meromorphic functions
• Doubly connected wandering domains for meromorphic functions
• Hyperbolic Dimension of Julia Sets of Meromorphic Maps with Logarithmic Tracts
• Hyperbolic dimension and radial Julia sets of transcendental functions
• Examples of Entire Functions with Pathological Dynamics
• Iteration of meromorphic functions
• Functions meromorphic outside a small set: completely invariant domains
• Dynamics in One Complex Variable. (AM-160)

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