Open AccessRadial distributions of Julia sets of difference operators of entire solutions of complex differential equations
Author(s) -
Jingjing Li,
AUTHOR_ID,
Zhicheng Huang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022286
Subject(s) - mathematics , julia set , measure (data warehouse) , limiting , entire function , transcendental equation , transcendental number , differential equation , polynomial , range (aeronautics) , transcendental function , mathematical analysis , function (biology) , differential operator , pure mathematics , discrete mathematics , computer science , mechanical engineering , materials science , database , evolutionary biology , engineering , composite material , biology
In this paper, we mainly investigate the radial distribution of Julia sets of difference operators of entire solutions of complex differential equation $ F(z)f^{n}(z)+P(z, f) = 0 $, where $ F(z) $ is a transcendental entire function and $ P(z, f) $ is a differential polynomial in $ f $ and its derivatives. We obtain that the set of common limiting directions of Julia sets of non-trivial entire solutions, their shifts have a definite range of measure. Moreover, an estimate of lower bound of measure of the set of limiting directions of Jackson difference operators of non-trivial entire solutions is given.