Complex dynamics in higher dimension. II. (English) Zbl 0847.58059

Fornaess, John Erik; Sibony, Nessim

Bloom, Thomas (ed.) et al., Modern methods in complex analysis. The Princeton conference in honor of Robert C. Gunning and Joseph J. Kohn, Princeton University, Princeton, NJ, USA, Mar. 16-20, 1992. Princeton, NJ: Princeton University Press. Ann. Math. Stud. 137, 135-182 (1995).

The authors continue the study of constructing a Fatou-Julia theory for holomorphic self map in \(P^2\) based on maps arising in two dimensions from Newton’s method. In fact they consider the problem in \(\mathbb{C}^2\) to find the zeros of a complex polynomial map and to study iteration of maps on \(P^2\). Then they interpret back down them in \(\mathbb{C}^2\).
[Part I: the authors, Astérisque 222, 201-231 (1994; Zbl 0813.58030).].
For the entire collection see [Zbl 0852.00026].

Reviewer: Y.Kozai (Tokyo)

MSC:

37F99	Dynamical systems over complex numbers
30D05	Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable

Keywords:

Fatou-Julia theory; holomorphic self map; iteration

Citations:

Zbl 0813.58030