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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.)

Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves

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Llibre, Jaume ; Messias, Marcelo ; Reinol, Alisson C.
Total Authors: 3
Document type: Journal article
Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 32, n. 3, p. 374-390, SEP 2017.
Web of Science Citations: 0

In this paper, we give the normal form of all planar polynomial vector fields of degree d 3 having two nonconcentric circles C-1 and C-2 as invariant algebraic curves and the function H=(C1C1 alpha)-C-beta with alpha and beta real values, as first integral. Moreover, we classify all global phase portraits on the Poincare disc of a subclass of these vector fields. (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