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# The real jacobian conjecture on $\R^2$ is true when one of the components has degree 3

• Let $F:\R^2\to \R^2$, $F=(p,q)$, 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.
Mathematics Subject Classification: Primary: 14R15; Secondary: 35F05, 35A30.

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