Steinness of the Fatou set for a rational map of the complex projective plane

Details Steinness of the Fatou set for a rational map of the complex projective plane Steinness of the Fatou set for a rational map of the complex projective plane

2006-04-04

arxiv.org/abs/math/0604060v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

For a dominant algebraically stable rational self-map of the complex
projective plane of degree at least 2, we will consider three different
definitions of Fatou set and show the equivalence of them. Consequently, it
follows that all Fatou components are Stein. This is an improvement of an early
result by Fornaess and Sibony.

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