Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains. (English) Zbl 0589.30022

Sullivan, Dennis

Ann. Math. (2) 122, 401-418 (1985).

This paper contains the detailed proof of the result, announced in the author’s paper [C. R. Acad. Sci., Paris, Sér. I 194, 301-303 (1982; Zbl 0496.30016)], that a rational mapping of the sphere has no wandering domains of normality. The methods introduced also allow a new proof of Ahlfors’ finiteness theorem in Kleinian groups.

Reviewer: I.N.Baker

MSC:

30D05	Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37B99	Topological dynamics

Keywords:

quasiconformal homeomorphisms; wandering domains; Kleinian groups

Citations:

Zbl 0496.30016