Newton polygons and B\"{o}ttcher coordinates near infinity for polynomial skew products

Abstract

Let $f(z,w)=(p(z),q(z,w))$ be a polynomial skew product such that the degrees of $p$ and $q$ are grater than or equal to $2$. Under one or two conditions, we prove that $f$ is conjugate to a monomial map on an invariant region near infinity. The monomial map and the region are determined by the degree of $p$ and a Newton polygon of $q$. Moreover, the region is included in the attracting basin of a superattracting fixed or indeterminacy point at infinity, or in the closure of the attracting basins of two point at infinity.