Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant

Llibre, Jaume; Messias, Marcelo [UNESP]; Reinol, Alisson de Carvalho [UNESP]

Artigo

Registro en:

http://www.worldscientific.com/doi/abs/10.1142/S0218127415500157

International Journal Of Bifurcation And Chaos, v. 25, n. 1, p. 16, 2015.

0218-1274

http://hdl.handle.net/11449/129339

10.1142/S0218127415500157

WOS:000349227400017

3757225669056317

https://repositorioslatinoamericanos.uchile.cl/handle/2250/8778679

Autor

Llibre, Jaume

Messias, Marcelo [UNESP]

Reinol, Alisson de Carvalho [UNESP]

Institución

Universidade Paulista Júlio de Mesquita Filho (Brasil)

Resumen

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.

MINECO/FEDER

AGAUR

ICREA Academia

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

UNESP Univ Estadual Paulista, Fac Ciencias &Tecnol, Dept Matemat &Comp, Sao Paulo, Brazil

MINECO/FEDER: MTM2008-03437

MINECO/FEDER: MTM201340998-P

AGAUR: 2013SGR-568

CAPES: 88881.030454/2013-01