Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces

• Autor(a) principal: Dalbelo, Thaís Maria [UNESP]
• Data de Publicação: 2018
• Outros Autores: Messias, Marcelo [UNESP], Reinol, Alisson C. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s00574-017-0045-9; http://hdl.handle.net/11449/174799
• topic: Darboux theory of integrability; Invariant algebraic surfaces; Polynomial differential systems; Singular varieties; Stratified vector fields; Vallis system; Weighted homogeneous surfaces

In this paper we give the normal form of all polynomial differential systems in R3 having a weighted homogeneous surface f= 0 as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when f= 0 is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface.