Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The Fatou set for critically finite maps

Author(s): Feng Rong
Journal: Proc. Amer. Math. Soc. 136 (2008), 3621-3625.
MSC (2000): Primary 32H50
Posted: 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 critically finite map on $\mathbf{P}^k$ is empty.

References:

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