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

Llibre, JaumeMessias, Marcelo [UNESP]Reinol, Alisson de Carvalho [UNESP]2015-10-212015-10-212015-01-01International Journal Of Bifurcation And Chaos, v. 25, n. 1, p. 16, 2015.0218-1274http://hdl.handle.net/11449/129339We 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.16engPolynomial differential systemsinvariant quadricDarboux integrabilityDarboux invariantNormal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux InvariantArtigo10.1142/S0218127415500157WOS:000349227400017Acesso restrito3757225669056317