Dynamics in the Eremenko-Lyubich class

DOI10.1090/ecgd/324zbMath1407.37068arXiv1709.09095OpenAlexW2963552629MaRDI QIDQ4687477

David J. Sixsmith

Publication date: 12 October 2018

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.09095

zbMATH Keywords

singular valueswandering domainsEremenko-Lyubich classEremenko conjecture

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 (16)

Fatou's associates ⋮ Complex flows, escape to infinity and a question of Rubel ⋮ Geometrically finite transcendental entire functions ⋮ The Eremenko–Lyubich constant ⋮ Speiser meets Misiurewicz ⋮ Entire functions with prescribed singular values ⋮ Bank-Laine functions with real zeros ⋮ Bank-Laine functions, the Liouville transformation and the Eremenko-Lyubich class ⋮ A complete realization of the orbits of generalized derivatives of quasiregular mappings ⋮ Singularities of inner functions associated with hyperbolic maps ⋮ Hairy Cantor sets ⋮ Prescribing the postsingular dynamics of meromorphic functions ⋮ Oscillating wandering domains for functions with escaping singular values ⋮ Variations on a theme of Hardy concerning the maximum modulus ⋮ Hausdorff dimension of escaping sets of meromorphic functions ⋮ The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class

Cites Work

• Brushing the hairs of transcendental entire functions
• A new characterisation of the Eremenko-Lyubich class
• Escaping endpoints explode
• Rigidity of escaping dynamics for transcendental entire functions
• Dynamic rays of bounded-type entire functions
• Entire functions with Julia sets of positive measure
• Dynamical properties of some classes of entire functions
• The dynamical fine structure of iterated cosine maps and a dimension paradox
• Hyperbolic entire functions with bounded Fatou components
• Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
• Complex dynamics
• On the singularities of the inverse to a meromorphic function of finite order
• A landing theorem for entire functions with bounded post-singular sets
• Univalent wandering domains in the Eremenko-Lyubich class
• Constructing entire functions by quasiconformal folding
• Trees and hairs for some hyperbolic entire maps of finite order
• Hyperbolic entire functions and the Eremenko-Lyubich class: Class \(\mathcal {B}\) or not class \(\mathcal {B}\)?
• Über das Nilradikal lokal kompakter Gruppen
• Non-autonomous conformal iterated function systems and Moran-set constructions
• The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics
• Semiconjugacies, pinched Cantor bouquets and hyperbolic orbifolds
• Models for the Eremenko–Lyubich class
• The Geometry of Julia Sets
• Entire functions with Julia sets of zero measure
• On plane dendroids and their end points in the classical sense
• Julia sets and bifurcation diagrams for exponential maps
• The Hausdorff dimension of Julia sets of entire functions
• Hausdorff dimension of hairs and ends for entire maps of finite order
• A landing theorem for dynamic rays of geometrically finite entire functions
• Are Devaney hairs fast escaping?
• On a question of Eremenko concerning escaping components of entire functions
• Hyperbolic Dimension of Julia Sets of Meromorphic Maps with Logarithmic Tracts
• The growth rate of an entire function and the Hausdorff dimension of its Julia set
• Dynamics of exp (z)
• Examples of Entire Functions with Pathological Dynamics
• Dynamics of entire functions near the essential singularity
• A finiteness theorem for a dynamical class of entire functions
• An explosion point for the set of endpoints of the Julia set of λ exp (z)
• On iterates of e^z
• The domains of normality of an entire function
• Iteration of a class of hyperbolic meromorphic functions
• Hausdorff dimension of the hairs without endpoints for λ exp z
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• The Hausdorff dimension of Julia sets of entire functions III
• ESCAPING POINTS OF EXPONENTIAL MAPS
• The Hausdorff Dimension of Julia Sets of Entire Functions IV
• Fast escaping points of entire functions
• Omitted Values in Domains of Normality
• The Hausdorff dimension of Julia sets of entire functions II
• Hyperbolic entire functions with full hyperbolic dimension and approximation by Eremenko-Lyubich functions
• Wandering domains for entire functions of finite order in the Eremenko–Lyubich class
• Lebesgue measure of escaping sets of entire functions
• Coding trees and boundaries of attracting basins for some entire maps
• Models for the Speiser class
• Quasiconformal Surgery in Holomorphic Dynamics
• Differentiable dynamical systems
• Dynamics in One Complex Variable. (AM-160)
• Topological dynamics of exponential maps on their escaping sets
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