Determination of Inverse Maps Related to the Jacobian Conjecture

Abstract

The Jacobian conjecture states that every polynomial map from ℂⁿ to ℂⁿ whose Jacobian determinant is a non-zero constant, then the map has a polynomial inverse. It is known that it suffices to prove the Jacobian conjecture for polynomial maps of the form X + H, with H_i being homogeneous, cubic or zero. In this article, we determine all the inverse maps of representative polynomials in the case n = 4.