Ludwik M. Drużkowski
(1997)
It is known that it is sufficient to consider in the Jacobian Conjecture only polynomial mappings of the form
,
where are homogeneous polynomials of degree 3 with real coefficients (or ), j = 1,...,n and H’(x) is a nilpotent matrix for each .
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
, where .
Note that the above inequality is not true when the coefficients...