An explosion point for the set of endpoints of the Julia set of λ exp (z)

DOI10.1017/S0143385700005460zbMath0668.58032WikidataQ121456328 ScholiaQ121456328MaRDI QIDQ3821323

John C. Mayer

Publication date: 1989

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

Cantor bouquetJulia setfanprime endexplosion pointdispersion pointsmooth fancomplex exponential functionexplosion space

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Related Items (23)

Distinguishing endpoint sets from Erdős space ⋮ Dynamics of generalised exponential maps ⋮ Iteration of meromorphic functions ⋮ Indecomposable continua in exponential dynamics ⋮ Trees and hairs for some hyperbolic entire maps of finite order ⋮ Non-escaping endpoints do not explode ⋮ Exotic topology in complex dynamics ⋮ A Characterization of Smooth Cantor Bouquets ⋮ On topological properties of Fatou sets and Julia sets of transcendental entire functions ⋮ Explosion points and topology of Julia sets of Zorich maps ⋮ Negligible sets in Erdős spaces ⋮ Escape rate and Hausdorff measure for entire functions ⋮ Generalized Mandelbrot and Julia Sets in a Family of Planar Angle-Doubling Maps ⋮ The Geometry of Julia Sets ⋮ Connectedness properties of the set where the iterates of an entire function are bounded ⋮ Itineraries of entire functions ⋮ Slow escaping points of meromorphic functions ⋮ Escaping endpoints explode ⋮ Dynamics in the Eremenko-Lyubich class ⋮ A note on the topology of escaping endpoints ⋮ Fatou’s web ⋮ Parameter Planes for Complex Analytic Maps ⋮ 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
• Wandering Domains in the Iteration of Entire Functions
• Complex analytic dynamics on the Riemann sphere
• The boundary of a simply connected domain
• Structural Instability of exp(z)
• Dynamics of entire functions near the essential singularity
• Area and Hausdorff Dimension of Julia Sets of Entire Functions

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