A sufficient condition in order that the real Jacobian conjecture in R^2 holds
Let F=(f,g):R2→R2 be a polynomial map such that detDF(x,y) is different from zero for all (x,y)∈R2 and F(0,0)=(0,0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of the polynomials ffx+ggx and ffy+ggy do not have real linear factors in common....
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/58388 |
| Acceso en línea: | https://doi.org/10.1016/j.jde.2015.12.011 http://hdl.handle.net/10459.1/58388 |
| Access Level: | acceso abierto |
| Palabra clave: | Real Jacobian conjecture Global injectivity Centre |
| Sumario: | Let F=(f,g):R2→R2 be a polynomial map such that detDF(x,y) is different from zero for all (x,y)∈R2 and F(0,0)=(0,0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of the polynomials ffx+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems. |
|---|