Topology of Fatou components for endomorphisms of CP^k: Linking with the Green's Current

Suzanne Lynch Hruska, Roland K. W. Roeder

Little is known about the global topology of the Fatou set $U(f)$ for holomorphic endomorphisms $f:{\mathbb{CP}}^k\to {\mathbb{CP}}^k$, when $k>1$. Classical theory describes $U(f)$…