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

Author(s)

Llibre, Jaume ; Messias, Marcelo ; Reinol, Alisson C.

• Document type: Journal article
• Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 32, n. 3, p. 374-390, SEP 2017.
• Web of Science Citations: 0

Abstract

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 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