The Fatou Set for Critically Finite Maps

الأصل · EN

It is a classical result in complex dynamics of one variable that the Fatou set for a critically finite map on P¹ consists of only basins of attraction for superattracting periodic points. In this paper we deal with critically finite maps on Pᵏ. We show that the Fatou set for a critically finite map on P² consists of only basins of attraction for superattracting periodic points. We also show that the Fatou set for a k-critically finite map on Pᵏ is empty.