Normal Forms for Polynomial Differential Systems in R^3 Having an Invariant Quadric and a Darboux Invariant
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo (FCT-UNESP (Brazil). Departamento de Matemática e Computacâo)
Reinol, Alisson C (FCT-UNESP (Brazil). Departamento de Matemática e Computacâo)

Additional title:	Polynomial differential systems in R^3 having an invariant quadric and a Darboux invariant
Date:	2015
Abstract:	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.
Grants:	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
Note:	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
Note:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux integrability ; Darboux invariant ; Invariant quadrics ; Polynomial differential systems
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25 Núm. 1 (2015) , p. 1550015, ISSN 1793-6551

DOI: 10.1142/S0218127415500157

Postprint 21 p, 502.4 KB

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