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| Home > Articles > Published articles > A new qualitative proof of a result on the real Jacobian conjecture |
(Universidade Federal de Sao Carlos Rod. Departamento de Matematica) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Date: | 2015 |
| Abstract: | Let F = (f, g) : R → R be a polynomial map such that det DF (x) is different from zero for all x ∈ R^2 . We assume that the degrees of f and g are equal. We denote by f and g the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If f and g do not have real linear factors in common, then F is injective. |
| Abstract: | Let F = (f, g) : R2 → R2 be a polynomial map such that det DF (x) is different from zero for all x ∈ R2 . We assume that the degrees of f and g are equal. We denote by f and g the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If f and g do not have real linear factors in common, then F is injective. |
| Grants: | Ministerio de Ciencia e Innovación MTM2008-03437 Ministerio de Ciencia e Innovación MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338 |
| Note: | Agraïments: FEDER-UNAB 10-4E-378. The two authors are also supported by a CAPES CSF-PVE grant 88881. 030454/ 2013-01 from the program CSF-PVE. |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Center ; Global injectivity ; Poincaré compactification ; Real Jacobian conjecture |
| Published in: | Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 3 (2015) , p. 1519-1524, ISSN 1678-2690 |
8 p, 263.7 KB |
