Siegel disks and periodic rays of entire functions

DOI10.1515/CRELLE.2008.081zbMath1162.30017arXivmath/0408041MaRDI QIDQ3542082

Lasse Rempe-Gillen

Publication date: 27 November 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408041

zbMATH Keywords

iterationJulia setcritical valueSiegel disk

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 (12)

About Rays, Dreadlocks and Periodic Points in Transcendental Dynamics ⋮ On the dynamics of a family of entire functions ⋮ Singular values and bounded Siegel disks ⋮ Rigidity of escaping dynamics for transcendental entire functions ⋮ A bound on the number of rationally invisible repelling orbits ⋮ A landing theorem for entire functions with bounded post-singular sets ⋮ A converse landing theorem in parameter spaces ⋮ Dynamic rays of bounded-type transcendental self-maps of the punctured plane ⋮ An entire transcendental family with a persistent Siegel disc ⋮ A separation theorem for entire transcendental maps ⋮ Siegel disks of the tangent family ⋮ Combinatorics of criniferous entire maps with escaping critical values

Cites Work

• Dynamics of the complex standard family
• Diophantine conditions imply critical points on the boundaries of Siegel disks of polynomials
• On questions of Fatou and Eremenko
• On a question of Eremenko concerning escaping components of entire functions
• On semiconjugation of entire functions
• ON A QUESTION OF HERMAN, BAKER AND RIPPON CONCERNING SIEGEL DISKS
• A landing theorem for periodic rays of exponential maps
• Research Problems in Complex Analysis

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