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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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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Abstract 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.
AbstractList 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.
Author Huang, Zhigang
Li, Jingjing
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Cites_doi 10.11650/twjm/1500404865
10.1112/jlms/s1-40.1.499
10.1016/j.jmaa.2013.07.026
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10.5186/aasfm.1975.0101
10.1016/j.jmaa.2011.10.016
10.1515/9783110863147
10.1017/S000497270002061X
10.1007/s11139-007-9101-1
10.1007/s10473-021-0415-7
10.1017/S1446788700014361
10.1016/j.jmaa.2005.04.010
10.1360/012014-32
10.1112/plms/s3-26.3.418
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SubjectTerms complex differential equations
difference operator
entire function
julia sets
radial distribution
Title Radial distributions of Julia sets of difference operators of entire solutions of complex differential equations
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