Polynomial Differential Systems in Having Invariant Weighted Homogeneous Surfaces

Author(s)

Dalbelo, Thais Maria ^[1] ; Messias, Marcelo ^[1] ; Reinol, Alisson C. ^[2]

Affiliation

^[1] UNESP Univ Estadual Paulista, Fac Ciencias & Tecnol, Dept Matemat & Computacao, Presidente Prudente, SP - Brazil

^[2] UNESP Univ Estadual Paulista, Intituto Biociencias Letras & Ciencias Exatas, Dept Matemat, Sao Jose Do Rio Preto, SP - Brazil

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 49, n. 1, p. 137-157, MAR 2018.
• Web of Science Citations: 0

Abstract

In this paper we give the normal form of all polynomial differential systems in having a weighted homogeneous surface 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 is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Nio 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. (AU)

• FAPESP's process: 13/26602-7 - Integrability and global dynamics of quadratic vector fields defined on R3 with Quadrics as invariant surfaces
• Grantee: Alisson de Carvalho Reinol
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants