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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.)

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

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Llibre, Jaume [1] ; Messias, Marcelo [2] ; Reinol, Alisson C. [3]
Total Authors: 3
[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
Total Affiliations: 3
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

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