Böttcher's equation
= Böttcher's equation
{c}
{title2=$\phi(f(z))=\phi(z)^m$}
{wiki}
<Böttcher's equation> asks for a holomorphic coordinate conjugating a map with a superattracting fixed point to a monomial. If $f(z)=az^m+O(z^{m+1})$ with $m\geq2$ and $a\ne0$, a normalized local solution has $\phi(z)=bz+O(z^2)$ with $b^{m-1}=a$. The <Böttcher theorem> asserts the existence and uniqueness of this local coordinate after choosing $b$.