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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Kazutoshi Maegawa
Journal: Proc. Amer. Math. Soc. 136 (2008), 2875-2879
MSC (2000): Primary 32H50; Secondary 32Q28
Published electronically: April 8, 2008
MathSciNet review: 2399053
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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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Additional Information

Kazutoshi Maegawa
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan
Email: maegawa@math.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09201-0
PII: S 0002-9939(08)09201-0
Keywords: Rational maps, Fatou sets, Stein manifolds
Received by editor(s): October 24, 2006
Received by editor(s) in revised form: April 17, 2007
Published electronically: April 8, 2008
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2008 American Mathematical Society