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January  2010, 26(1): 75-87. doi: 10.3934/dcds.2010.26.75

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, Brazil, Brazil

Received  January 2009 Revised  June 2009 Published  October 2009

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.
Keywords: Global solvability., Real jacobian conjecture, Global injectivity.
Mathematics Subject Classification: Primary: 14R15; Secondary: 35F05, 35A3.
Citation: Francisco Braun, José Ruidival dos Santos Filho. The real jacobian conjecture on $\R^2$ is true when one of the components has degree 3. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 75-87. doi: 10.3934/dcds.2010.26.75
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