On radial distributions of Julia sets of Newton's method of solutions of complex differential equations
type: Item
instance of: scholarly article
title: On radial distributions of Julia sets of Newton's method of solutions of complex differential equations
zbMATH Open document ID: 1372.30014
author: Guowei Zhang
author: Lianzhong Yang
published in: Proceedings of the Japan Academy. Series A
publication date: 2016-05-27T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1451330559
review text: By using the classical Newton method for finding the zeros for an entire function and Nevanlinna theory in angular domains, the authors study the radial distribution of Julia sets of certain Riccati equations, and prove the following result: Suppose \(f\) is a transcendental meromorphic solution of the Riccati equation \(f'(z)+A(z)(f(z)-z)^2=0\), where \(A(z)\) is a transcendental entire function of finite order \(\sigma (f)\). Then \(\mathrm{mes\,}\Delta(f)\geq \min\{2\pi, \pi/\sigma (f)\}\). This result improves and extends the corresponding results from the references [\textit{Z.-G. Huang} and \textit{J. Wang}, J. Math. Anal. Appl. 409, No. 1, 478--484 (2014; Zbl 1314.34174); ibid. 387, No. 2, 1106--1113 (2012; Zbl 1238.37012)] given in the present paper. The results of the present paper are very interesting. The analysis and the reasoning of the present paper is new and deep.
reviewed by: Xiao-Min Li
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F50
zbMATH DE Number: 6586127
zbMATH Keywords: entire functions
zbMATH Keywords: Riccati equations
zbMATH Keywords: Julia sets
MaRDI profile type: Publication
OpenAlex ID: W2205709462
Wikidata QID: Q120800475
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DOI: 10.3792/PJAA.92.1
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description: scientific article; zbMATH DE number 6586127