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The dynamics of Newton’s method. (English) Zbl 0853.58086
Devaney, Robert L. (ed.), Complex dynamical systems. The mathematics behind the Mandelbrot and Julia sets. Lecture notes prepared for the American Mathematical Society short course, held in Cincinnati, OH, USA, January 10-11, 1994. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 49, 139-154 (1994).
This is a short discussion of known results about the dynamics of Newton’s map for rational functions and polynomial-like maps. It concentrates mainly on results of {\it J. H. Curry, L. Garnett} and {\it D. Sullivan} [Commun. Math. Phys. 91, 267-277 (1983; Zbl 0524.65032)] and {\it A. Douady} and {\it J. H. Hubbard} [Ann. Sci. Éc. Norm. Supér., Sér. 18, 287-343 (1985; Zbl 0587.30028)]. For the entire collection see [Zbl 0809.00024].

37F99Complex dynamical systems
30D05Functional equations in the complex domain, iteration and composition of analytic functions
65H05Single nonlinear equations (numerical methods)