Escape rate and Hausdorff measure for entire functions

DOI10.1007/s00209-012-1085-xzbMath1279.30044arXiv1203.0190OpenAlexW3100108098MaRDI QIDQ1955727

Jörn Peter, Walter Bergweiler

Publication date: 18 June 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0190

zbMATH Keywords

entire functionHausdorff dimensiongauge functionescape rateescaping set

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) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (7)

Slow escaping points of quasiregular mappings ⋮ On the dimension of points which escape to infinity at given rate under exponential iteration ⋮ Dimensions of slowly escaping sets and annular itineraries for exponential functions ⋮ Hausdorff measure of the escaping parameter without endpoints is zero for exponential family ⋮ On the set where the iterates of an entire function are neither escaping nor bounded ⋮ On slow escaping and non-escaping points of quasimeromorphic mappings ⋮ Fatou’s web

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Karpińska's paradox in dimension 3
• Dynamic rays of bounded-type entire functions
• Dynamical properties of some classes of entire functions
• A transcendental Julia set of dimension 1
• Slow escaping points of meromorphic functions
• On questions of Fatou and Eremenko
• Entire functions with Julia sets of zero measure
• HOW POINTS ESCAPE TO INFINITY UNDER EXPONENTIAL MAPS
• Dynamics of meromorphic functions with direct or logarithmic singularities
• Hausdorff dimension of hairs and ends for entire maps of finite order
• Hausdorff dimensions of escaping sets of transcendental entire functions
• On the Hausdorff dimension of the Julia set of a regularly growing entire function
• Are Devaney hairs fast escaping?
• Hausdorff measure of Julia sets in the exponential family
• Hyperbolic Dimension of Julia Sets of Meromorphic Maps with Logarithmic Tracts
• Hyperbolic dimension and radial Julia sets of transcendental functions
• The growth rate of an entire function and the Hausdorff dimension of its Julia set
• Dynamics of exp (z)
• 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)
• The domains of normality of an entire function
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• Maximum curves and isolated points of entire functions
• The Hausdorff Dimension of Julia Sets of Entire Functions IV
• Fast escaping points of entire functions
• The Hausdorff dimension of Julia sets of entire functions II
• Hyperbolic entire functions with full hyperbolic dimension and approximation by Eremenko-Lyubich functions

This page was built for publication: Escape rate and Hausdorff measure for entire functions