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.
Citation: Jingjing Li, Zhigang Huang. Radial distributions of Julia sets of difference operators of entire solutions of complex differential equations[J]. AIMS Mathematics, 2022, 7(4): 5133-5145. doi: 10.3934/math.2022286
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.
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Jingjing Li, Zhigang Huang. Radial distributions of Julia sets of difference operators of entire solutions of complex differential equations[J]. AIMS Mathematics, 2022, 7(4): 5133-5145. doi: 10.3934/math.2022286
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