Polynomial Vector Fields on Algebraic Surfaces of Revolution

Autor(es)

Dias, Fabio Scalco ^[1] ; Mello, Luis Fernando ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Itajuba, Inst Matemat & Computac, Ave BPS 1303, BR-37500903 Itajuba, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Results in Mathematics; v. 76, n. 1 MAR 2021.
• Citações Web of Science: 0

Resumo

In the first part of the article we study polynomial vector fields of arbitrary degree in R3 having an algebraic surface of revolution invariant by their flows. In the second part, we restrict our attention to an important case where the algebraic surface of revolution is a cubic surface. We characterize all the possible configurations of invariant meridians and parallels that the vector fields can exhibit. Additionally we shall consider when the invariant parallels can be limit cycles. The results obtained in the second part can be adapted to the general surfaces studied in the first part. (AU)

• Processo FAPESP: 19/07316-0 - Teoria de singularidades e aplicações a geometria diferencial, equações diferenciais e visão computacional
• Beneficiário: Farid Tari
• Modalidade de apoio: Auxílio à Pesquisa - Temático