Lebesgue measure of escaping sets of entire functions of completely regular growth

DOI10.1112/jlms/jdw051zbMath1352.37134arXiv1510.03628OpenAlexW3100501333MaRDI QIDQ2835340

Walter Bergweiler, I. E. Chyzhykov

Publication date: 2 December 2016

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.03628

zbMATH Keywords

linear differential equationsJulia setLebesgue measureescaping set

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (6)

Unnamed Item ⋮ ON THE ITERATIONS AND THE ARGUMENT DISTRIBUTION OF MEROMORPHIC FUNCTIONS ⋮ Exponential polynomials with Fatou and non-escaping sets of finite Lebesgue measure ⋮ Fast growth entire functions whose escaping set has Hausdorff dimension two ⋮ Lebesgue measure of escaping sets of entire functions ⋮ Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exceptional values of solutions of linear differential equations
• Entire functions with Julia sets of positive measure
• Dynamical properties of some classes of entire functions
• Analog of the Valiron-Titchmarsh theorem for two-term asymptotics of subharmonic functions with masses on a finite system of rays
• Asymptotic behavior of logarithmic derivative of entire function of completely regular growth
• Meromorphic functions of completely regular growth and their logarithmic derivatives
• On multiply-connected Fatou components in iteration of meromorphic functions
• On questions of Fatou and Eremenko
• Julia and Escaping Set Spiders’ Webs of Positive Area
• 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
• Hyperbolic dimension and radial Julia sets of transcendental functions
• The growth rate of an entire function and the Hausdorff dimension of its Julia set
• On semiconjugation of entire functions
• Iteration of meromorphic functions
• Fast escaping points of entire functions
• Functions of genus zero for which the fast escaping set has Hausdorff dimension two
• Inequalities for the Logarithmic Derivatives of a Polynomial

This page was built for publication: Lebesgue measure of escaping sets of entire functions of completely regular growth