Dynamics of symmetric holomorphic maps on projective spaces

Abstract

We consider complex dynamics of a critically finite} holomorphic map from $\mathbf{P}^{k}$ to $\mathbf{P}^{k}$, which has symmetries associated with the symmetric group $S_{k+2}$ acting on $\mathbf{P}^{k}$, for each $k \ge 1$. The Fatou set of each map of this family consists of attractive basins of superattracting points. Each map of this family satisfies Axiom A.