Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine

Author(s)

Llibre, Jaume ^[1] ; Messias, Marcelo ^[2] ; Reinol, Alisson C. ^[3]

Affiliation

^[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Catalonia - Spain

^[2] Univ Estadual Paulista, UNESP, Fac Ciencias & Tecnol, Dept Matemat & Computacao, Presidente Prudente, SP - Brazil

^[3] Univ Estadual Paulista, UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, Sao Jose Do Rio Preto, SP - Brazil

• Document type: Journal article
• Source: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO; v. 67, n. 3, p. 569-580, DEC 2018.
• Web of Science Citations: 0

Abstract

In this paper we consider all the quadratic polynomial differential systems in having exactly nine invariant planes taking into account their multiplicities. This is the maximum number of invariant planes that these kind of systems can have, without taking into account the infinite plane. We prove that there exist thirty possible configurations for these invariant planes, and we study the realization and the existence of first integrals for each one of these configurations. We show that at least twenty three of these configurations are realizable and provide explicit examples for each one of them. (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: 16/01258-0 - Quadratic vector fields defined in R3 with invariant planes
• Grantee: Alisson de Carvalho Reinol
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants