Fornaess–Stensønes basin conjecture for uniformly attracting sequences

Let $(f_n)$ be a sequence of automorphisms of $\mathbb C^m$ satisfying

$$C\|z\|\leq \|f_n(z)\|\leq D\|z\|$$

for every $n\in\mathbb N$ and every $z$ in the unit ball $\mathbb B$, where $1>D>C>0$ are independent of $n$. Such a sequence is uniformly attracting, and define its basin of attraction by

$$\Omega=\Omega_{(f_n)}=\{z\in\mathbb C^m\mid f_n\circ\cdots\circ f_0(z)\rightarrow 0\}.$$

Fornaess–Stensønes basin conjecture. The basin $\Omega$ is always biholomorphic to $\mathbb C^m$. A positive answer would imply a positive answer to Bedford's stable-manifold conjecture; the paper presents this basin statement as an unresolved conjecture.