Radial distributions of Julia sets of difference operators of entire solutions of complex differential equations

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 deriv...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 4; pp. 5133 - 5145
Main Authors Li, Jingjing, Huang, Zhigang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
complex differential equations
difference operator
entire function
julia sets
radial distribution
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022286

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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022286