Real Jacobian mates

Abstract

Let $p$ be a real polynomial in two variables. We say that a polynomial $q$ is a real Jacobian mate of $p$ if the Jacobian determinant of the mapping $(p,q):{\mathbb{R}}^2\to {\mathbb{R}}^2$ is everywhere positive. We present a class of polynomials that do not have real Jacobian mates.

References in corpus (1)

• On polynomial submersions of degree $4$ and the real Jacobian conjecture in ${\mathbb{R}}^2$