Lebesgue measure of Julia sets and escaping sets of certain entire functions
Volume 242 / 2018
Fundamenta Mathematicae 242 (2018), 281-301
MSC: Primary 37F10; Secondary 30D05.
DOI: 10.4064/fm477-11-2017
Published online: 1 June 2018
Abstract
We give criteria for the escaping set and the Julia set of an entire function to have positive measure. The results are applied to Poincaré functions of semihyperbolic polynomials and to the Weierstraß $\sigma $-function.
