In an already answered question regarding the Fatou-Julia theorem (every basin of attraction contains a critical point), I saw that a user stated:
There are some other situations where an analogous theorem applies. For instance, if you define everything correctly it holds for nonivertible holomorphic maps on higher dimensional projective spaces as well, but this is harder.
Does someone know where to find a proof for this? Specifically, I want to use it on a function $f: \mathbb{R}^4 \to \mathbb{R}^4$ with nice properties.
Thank you.