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

 

The Fatou set for critically finite maps


Author: Feng Rong
Journal: Proc. Amer. Math. Soc. 136 (2008), 3621-3625
MSC (2000): Primary 32H50
Published electronically: May 19, 2008
MathSciNet review: 2415046
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Abstract: It is a classical result in complex dynamics of one variable that the Fatou set for a critically finite map on $ \mathbf{P}^1$ consists of only basins of attraction for superattracting periodic points. In this paper, we deal with critically finite maps on $ \mathbf{P}^k$. We show that the Fatou set for a critically finite map on $ \mathbf{P}^2$ consists of only basins of attraction for superattracting periodic points. We also show that the Fatou set for a $ k-$critically finite map on $ \mathbf{P}^k$ is empty.


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Additional Information

Feng Rong
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email: frong@syr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09358-1
PII: S 0002-9939(08)09358-1
Received by editor(s): July 17, 2007
Received by editor(s) in revised form: September 13, 2007
Published electronically: May 19, 2008
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.