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

F. Braun, B. Oréfice-Okamoto

The main result of this paper is the following version of the real Jacobian conjecture: "Let $F=(p,q):{\mathbb{R}}^2\to {\mathbb{R}}^2$ be a polynomial map with nowhere zero Jacobian determinant. If th…