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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.
Kohei Ueno (Sun,) studied this question.
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