Non-autonomous basin biholomorphism conjecture

Let $f_1,f_2,\ldots$ be a sequence of automorphisms of $\mathbb{C}^k$. Assume that there exist constants $0<a<b<1$ such that, for every $n$ and every $z$ in the unit ball, one has

$$a\|z\|\leq \|f_n(z)\|\leq b\|z\|.$$

The basin of attraction of $0$ for this sequence is the set of points $z\in\mathbb{C}^k$ such that $f_n\circ\cdots\circ f_1(z)\to 0$. Non-autonomous basin conjecture. This basin is biholomorphically equivalent to $\mathbb{C}^k$. A positive answer would imply Bedford's stable-manifold conjecture. The paper presents this as a conjecture and does not state a resolution.