The Fatou Set for Critically Finite Maps

Feng Rong

The Fatou Set for Critically Finite Maps

Dynamical Systems 2007-05-23 v1 Complex Variables

Authors: Feng Rong

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.

Keywords

thurston maps

Cite

@article{arxiv.math/0608477,
  title  = {The Fatou Set for Critically Finite Maps},
  author = {Feng Rong},
  journal= {arXiv preprint arXiv:math/0608477},
  year   = {2007}
}

Comments

5 pages

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