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Pàgina inicial > Articles > Articles publicats > Normal Forms for Polynomial Differential Systems in R^3 Having an Invariant Quadric and a Darboux Invariant |
Títol variant: | Polynomial differential systems in R^3 having an invariant quadric and a Darboux invariant |
Data: | 2015 |
Resum: | We give the normal forms of all polynomial differential systems in R^3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux invariant constructed uniquely using the invariant quadric, giving explicitly their expressions. As an example, we apply the obtained results in the determination of the Darboux invariants for the Chen system with an invariant quadric. |
Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 European Commission 316338 European Commission 318999 |
Nota: | El títol de la versió pre-print de l'article és: Polynomial differential systems in R^3 having an invariant quadric and a Darboux invariant |
Nota: | Agraïments: FEDER-UNAB-10-4E-378. The second author is supported by CNPq-Brazil grant 30 8315/2012-0 and by FAPESP grant 12/18413-7. The third author is supported by FAPESP grant 2013/01743-7. All the authors are supported by the Int.Coop. Proj. CAPES/MECD-TQED II and PHB-2009-0025. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Darboux integrability ; Darboux invariant ; Invariant quadrics ; Polynomial differential systems |
Publicat a: | International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25 Núm. 1 (2015) , p. 1550015, ISSN 1793-6551 |
Postprint 21 p, 502.4 KB |