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

Llibre, Jaume; Messias, Marcelo; Reinol, Alisson de Carvalho

Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/11449/129339

Title:

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

Author(s):

Institution:

Univ Autonoma Barcelona
Universidade Estadual Paulista (UNESP)

ISSN:

0218-1274

Sponsorship:

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)

Sponsorship Process Number:

MINECO/FEDER: MTM2008-03437
MINECO/FEDER: MTM201340998-P
AGAUR: 2013SGR-568
CAPES: 88881.030454/2013-01
CNPq: 308315/2012-0
FAPESP: 12/18413-7
FAPESP: 2013/01743-7
: PHB-2009-0025

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.

Issue Date:

1-Jan-2015

Citation:

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

Time Duration:

16

Publisher:

World Scientific Publ Co Pte Ltd

Keywords:

Polynomial differential systems
invariant quadric
Darboux integrability
Darboux invariant

Source:

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

URI:

Access Rights:

Acesso restrito

Type:

outro

Source:

http://repositorio.unesp.br/handle/11449/129339

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