The Fatou set for critically finite maps
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- Proc. Amer. Math. Soc. 136 (2008), 3621-3625 Request permission
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.References
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Additional Information
- Feng Rong
- Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
- Email: frong@syr.edu
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3621-3625
- MSC (2000): Primary 32H50
- DOI: https://doi.org/10.1090/S0002-9939-08-09358-1
- MathSciNet review: 2415046