EN
It is known that it is sufficient to consider in the Jacobian Conjecture only polynomial mappings of the form
$F(x₁,...,x_n) = x - H(x) := (x₁ - H₁(x₁,...,x_n),...,x_n - H_n(x₁,...,x_n))$,
where $H_j$ are homogeneous polynomials of degree 3 with real coefficients (or $H_j = 0$), j = 1,...,n and H'(x) is a nilpotent matrix for each $x = (x₁,...,x_n) ∈ ℝ^n$.
We give another proof of Yu's theorem that in the case of non-negative coefficients of H the mapping F is a polynomial automorphism, and we moreover prove that in that case
$deg F^{-1} ≤ (deg F)^{ind F - 1}$, where $ind F := max{ind H'(x): x ∈ ℝ^n}$.
Note that the above inequality is not true when the coefficients of H are arbitrary real numbers; cf. [E3].