Proceedings of the Japan Academy, Series A, Mathematical Sciences

On radial distributions of Julia sets of Newton’s method of solutions of complex differential equations

Guowei Zhang and Lianzhong Yang

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In this paper we mainly investigate the radial distribution of Julia sets of Newton’s method of entire solutions of some complex linear differential equations. Under certain conditions, we find the lower bound of it and also obtain some related results.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 1 (2016), 1-6.

First available in Project Euclid: 28 December 2015

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Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets

Radial distribution Julia set Newton’s method complex differential equation


Zhang, Guowei; Yang, Lianzhong. On radial distributions of Julia sets of Newton’s method of solutions of complex differential equations. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 1, 1--6. doi:10.3792/pjaa.92.1.

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