Ascoli-Arzelà type theorem for rational iterations on the complex projective plane

Maegawa, Kazutoshi

doi:10.1090/S0002-9939-08-09201-0

Ascoli-Arzelà type theorem for rational iterations on the complex projective plane
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Proc. Amer. Math. Soc. 136 (2008), 2875-2879 Request permission

Abstract:

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 the Fatou set and show the equivalence of them (Ascoli-Arzelà type theorem). As a corollary, it follows that all Fatou components are Stein. This is an improvement of an early result by Fornæss and Sibony.

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