The real Jacobian conjecture on \(\mathbb R^2\) is true when one of the components has degree 3. (English) Zbl 1181.14067
Summary: Let \(F:\mathbb R^2\to \mathbb R^2, F=(p,q)\), be a polynomial mapping such that det \(DF\) never vanishes. In this paper it is shown that if either \(p\) or \(q\) has degree less or equal 3, then \(F\) is injective. The technique relates solvability of appropriate vector fields with injectivity of the mapping.
MSC:
| 14R15 | Jacobian problem |
| 35F05 | Linear first-order PDEs |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
