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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Polynomial Differential Systems in Having Invariant Weighted Homogeneous Surfaces

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Dalbelo, Thais Maria [1] ; Messias, Marcelo [1] ; Reinol, Alisson C. [2]
Total Authors: 3
[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
Total Affiliations: 2
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

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 type: Scholarships in Brazil - Doctorate
FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support type: Research Projects - Thematic Grants