Brushing the hairs of transcendental entire functions

DOI10.1016/j.topol.2012.02.004zbMath1267.37041arXiv1101.4209OpenAlexW2132069773WikidataQ113397028 ScholiaQ113397028MaRDI QIDQ411811

Krzysztof Barański, Xavier Jarque, Lasse Rempe-Gillen

Publication date: 30 April 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4209

zbMATH Keywords

Julia setescaping setEremenko-Lyubich classstraight brush

Mathematics Subject Classification ID

Related Items (18)

Topological dynamics of cosine maps ⋮ Nowhere differentiable hairs for entire maps ⋮ Dynamics of generalised exponential maps ⋮ Convergence of rays with rational argument in hyperbolic components—an illustration in transcendental dynamics ⋮ Non-escaping endpoints do not explode ⋮ Explosion points and topology of Julia sets of Zorich maps ⋮ Geometrically finite transcendental entire functions ⋮ Dynamic rays of bounded-type entire functions ⋮ A converse landing theorem in parameter spaces ⋮ Connectedness properties of the set where the iterates of an entire function are bounded ⋮ Dynamic rays of bounded-type transcendental self-maps of the punctured plane ⋮ Escaping endpoints explode ⋮ Speiser class Julia sets with dimension near one ⋮ Escaping points in the boundaries of Baker domains ⋮ Dynamics in the Eremenko-Lyubich class ⋮ Cantor bouquets in spiders’ webs ⋮ Eremenko points and the structure of the escaping set ⋮ Criniferous entire maps with absorbing Cantor bouquets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rigidity of escaping dynamics for transcendental entire functions
• Dynamic rays of bounded-type entire functions
• Dynamical properties of some classes of entire functions
• Complex dynamics
• The finer geometry and dynamics of the hyperbolic exponential family
• Trees and hairs for some hyperbolic entire maps of finite order
• Semiconjugacies, pinched Cantor bouquets and hyperbolic orbifolds
• The Geometry of Julia Sets
• Hausdorff dimension of hairs and ends for entire maps of finite order
• Hausdorff dimensions of escaping sets of transcendental entire functions
• A landing theorem for dynamic rays of geometrically finite entire functions
• On a question of Eremenko concerning escaping components of entire functions
• Dynamics of exp (z)
• Dynamics of entire functions near the essential singularity
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• Hausdorff dimension of the hairs without endpoints for λ exp z
• ESCAPING POINTS OF EXPONENTIAL MAPS
• The Hausdorff Dimension of Julia Sets of Entire Functions IV
• A Characterization of Smooth Cantor Bouquets
• Topological dynamics of exponential maps on their escaping sets
• The Kline sphere characterization problem
• Accessible points in the Julia sets of stable exponentials.

This page was built for publication: Brushing the hairs of transcendental entire functions