  In this article we analyze the global diffeomorphism property of polynomial
maps $F:\mathbb{R}^n\rightarrow\mathbb{R}^n$ by studying the properties of the
Newton polytopes at infinity corresponding to the sum of squares polynomials
$\|F\|_2^2$. This allows us to identify a class of polynomial maps $F$ for
which their global diffeomorphism property on $\mathbb{R}^n$ is equivalent to
their Jacobian determinant $\text{det }JF$ vanishing nowhere on $\mathbb{R}^n$.
In other words, we identify a class of polynomial maps for which the Real
Jacobian Conjecture, which was proven to be false in general, still holds.
