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

Francisco Braun; José Ruidival dos Santos Filho

doi:10.3934/dcds.2010.26.75

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2010, Volume 26, Issue 1: 75-87. Doi: 10.3934/dcds.2010.26.75

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

Francisco Braun^1, and
José Ruidival dos Santos Filho^1,

1.
Departamento de Matemática, Universidade Federal de São Carlos, Rod. Washington Luís, Km 235 - C.P. 676 - 13565-905, São Carlos, SP

Received: December 31, 2008

Revised: May 31, 2009

Published: February 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 14R15; Secondary: 35F05, 35A30.

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