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Ascoli-Arzelà type theorem for rational iterations on the complex projective plane
Author(s):
Kazutoshi
Maegawa
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2875-2879.
MSC (2000):
Primary 32H50;
Secondary 32Q28
Posted:
April 8, 2008
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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.
References:
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- S. IVASHKOVICH, On convergence properties of meromorphic functions and mappings. (Russian), Complex analysis in modern mathematics, FAZIS, Moscow, 2001, 133-151. English manuscript available at ArXiv math.CV/9804007. MR 1833510 (2002e:32023)
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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:
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
Posted:
April 8, 2008
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2008,
American Mathematical Society
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