The Geometry of Julia Sets

DOI10.2307/2154434zbMath0809.54034OpenAlexW4250876049MaRDI QIDQ3137504

Lex G. Oversteegen, Jan M. Aarts

Publication date: 30 March 1995

Full work available at URL: https://doi.org/10.2307/2154434

zbMATH Keywords

Julia setsCantor bouquetexponential mappingshairy arcs

Mathematics Subject Classification ID

Related Items (48)

Topological dynamics of cosine maps ⋮ A characterization of Erdős space factors ⋮ Distinguishing endpoint sets from Erdős space ⋮ Brjuno numbers and the symbolic dynamics of the complex exponential ⋮ Joining polynomial and exponential combinatorics for some entire maps ⋮ Dynamics of generalised exponential maps ⋮ Iteration of meromorphic functions ⋮ On the set function \(\mathcal R\) ⋮ Trees and hairs for some hyperbolic entire maps of finite order ⋮ Non-escaping endpoints do not explode ⋮ Exotic topology in complex dynamics ⋮ On the dimension of points which escape to infinity at given rate under exponential iteration ⋮ Homogeneity degree of fans ⋮ The topological dimension of radial Julia sets ⋮ Rigidity of escaping dynamics for transcendental entire functions ⋮ Arithmetic geometric model for the renormalisation of irrationally indifferent attractors ⋮ Explosion points and topology of Julia sets of Zorich maps ⋮ Brushing the hairs of transcendental entire functions ⋮ Geometrically finite transcendental entire functions ⋮ Dynamic rays of bounded-type entire functions ⋮ Negligible sets in Erdős spaces ⋮ Hausdorff dimension of hairs and ends for entire maps of finite order ⋮ Generalized Mandelbrot and Julia Sets in a Family of Planar Angle-Doubling Maps ⋮ Weak chainability of arc folders ⋮ Itineraries of entire functions ⋮ Dynamic rays of bounded-type transcendental self-maps of the punctured plane ⋮ Do Diophantine vectors form a Cantor bouquet? ⋮ Lee-Yang zeros for the DHL and 2D rational dynamics. I: Foliation of the physical cylinder ⋮ Escaping endpoints explode ⋮ Speiser class Julia sets with dimension near one ⋮ Perturbations in the Speiser class ⋮ Escaping points in the boundaries of Baker domains ⋮ \(Se^x\): dynamics, topology, and bifurcations of complex exponentials ⋮ HAIRS FOR THE COMPLEX EXPONENTIAL FAMILY ⋮ Classification of escaping exponential maps ⋮ A Recurrent Nonrotational Homeomorphism on the Annulus ⋮ Dynamics in the Eremenko-Lyubich class ⋮ The space of Lelek fans in the Cantor fan is homeomorphic to Hilbert space ⋮ Unnamed Item ⋮ Cantor bouquets in spiders’ webs ⋮ Unnamed Item ⋮ A note on the topology of escaping endpoints ⋮ Criniferous entire maps with absorbing Cantor bouquets ⋮ Semiconjugacies, pinched Cantor bouquets and hyperbolic orbifolds ⋮ Hairy Cantor sets ⋮ Building blocks for quadratic Julia sets ⋮ Dynamical convergence of polynomials to the exponential ⋮ Interactions of the Julia Set with Critical and (Un)Stable Sets in an Angle-Doubling Map on ℂ\{0}

Cites Work

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• Uniformization of attracting basins for exponential maps
• The boundary of a simply connected domain
• On plane dendroids and their end points in the classical sense
• Julia sets and bifurcation diagrams for exponential maps
• Dynamics of exp (z)
• Structural Instability of exp(z)
• Dynamics of entire functions near the essential singularity
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• An explosion point for the set of endpoints of the Julia set of λ exp (z)
• On iterates of e^z
• A Recurrent Nonrotational Homeomorphism on the Annulus
• e^z: DYNAMICS AND BIFURCATIONS
• A Characterization of Smooth Cantor Bouquets

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