The dynamical Ax–Lindemann–Weierstrass conjecture for Böttcher coordinates

Let $f$ be a non-exceptional polynomial of degree $d\ge 2$. Let $V_1\subset \mathbb{C}^n$ be an irreducible subvariety with non-empty intersection with $\mathbb{D}_R^n$, and let $V_1'$ be a branch of $V_1$ contained in $\mathbb{D}_R^n$. The dynamical Ax–Lindemann–Weierstrass conjecture. The Zariski closure

$$\overline{\mathbf{\Psi}_{f,n}(V_1')}^{\operatorname{Zar}}$$

is $f$-special. This is proposed by analogy with the Ax–Lindemann–Weierstrass theorem and is intended to describe algebraic images of branches under the Böttcher-coordinate map; the source gives no resolution status.