Fatou’s web

DOI10.1090/proc/13150zbMath1351.37183arXiv1510.07449OpenAlexW2963458001MaRDI QIDQ2827372

Vasiliki Evdoridou

Publication date: 19 October 2016

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

Full work available at URL: https://arxiv.org/abs/1510.07449

zbMATH Keywords

escaping setspider's webFatou's function

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 (12)

Fatou's associates ⋮ Periodic domains of quasiregular maps ⋮ Non-escaping endpoints do not explode ⋮ The topological dimension of radial Julia sets ⋮ Spiders' webs in the punctured plane ⋮ On the level of \(Q_{\epsilon} (f)\) in quite fast escaping set and spider's web ⋮ On the connectivity of the escaping set in the punctured plane ⋮ Escaping endpoints explode ⋮ Spiders' webs of doughnuts ⋮ Dynamical sets whose union with infinity is connected ⋮ The iterated minimum modulus and conjectures of Baker and Eremenko ⋮ Eremenko points and the structure of the escaping set

Cites Work

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• Baker's conjecture and Eremenko's conjecture for functions with negative zeros
• The fast escaping set for quasiregular mappings
• Escaping endpoints explode
• Mini-workshop: The escaping set in transcendental dynamics. Abstracts from the mini-workshop held December 6th -- December 12th, 2009
• The finer geometry and dynamics of the hyperbolic exponential family
• Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps
• Escape rate and Hausdorff measure for entire functions
• Escaping points in the boundaries of Baker domains
• Trees and hairs for some hyperbolic entire maps of finite order
• The dynamics and geometry of the Fatou functions
• Poincaré functions with spiders’ webs
• Slow escaping points of meromorphic functions
• Entire functions for which the escaping set is a spider's web
• On questions of Fatou and Eremenko
• Hyperbolic dimension and radial Julia sets of transcendental functions
• An explosion point for the set of endpoints of the Julia set of λ exp (z)
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• Fast escaping points of entire functions
• Invariant domains and singularities
• On Fixed Point Properties of Plane Continua

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