A new qualitative proof of a result on the real Jacobian conjecture
Braun, Francisco (Universidade Federal de Sao Carlos Rod. Departamento de Matematica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha:	2015
Resumen:	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.
Resumen:	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.
Ayudas:	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
Nota:	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.
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	Center ; Global injectivity ; Poincaré compactification ; Real Jacobian conjecture
Publicado en:	Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 3 (2015) , p. 1519-1524, ISSN 1678-2690

DOI: 10.1590/0001-3765201520130408

Postprint 8 p, 263.7 KB

El registro aparece en las colecciones:
Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
Artículos > Artículos de investigación
Artículos > Artículos publicados