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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Fatou set for critically finite maps
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by Feng Rong PDF
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.
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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