Böttcher coordinates at wild superattracting fixed points

Hang Fu, Hongming Nie

Let $p$ be a prime number, let $g(x)=x^{p^2}+p^{r+2}{x}^{p^2+1}$ with $r\in {\mathbb{Z}}_{\ge 0}$, and let $\varphi (x)=x+O(x^2)$ be the Böttcher coordinate satisfying $ϕ(g(x))=ϕ(x)^{p^{…