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Integrability of two-dimensional polynomial differential systems

Grant number: 13/01743-7
Support type:Scholarships abroad - Research Internship - Master's degree
Effective date (Start): April 15, 2013
Effective date (End): June 14, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Marcelo Messias
Grantee:Alisson de Carvalho Reinol
Supervisor abroad: Jaume Llibre
Home Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
Research place: Universitat Autònoma de Barcelona (UAB), Spain  
Associated to the scholarship:11/16154-1 - Global analysis of Quadratic Planar Polynomial Vector Fields with Invariant Algebraic Surfaces, BP.MS


We propose the study of certain techniques of integrability of planar polynomial vector fields, in the context of Darboux Integrability Theory. To apply these techniques in the global analysis of phase portraits of quadratic and cubic vector fields having certain types of invariant algebraic curves (parabolas, elipses, hyperbolas, and other). In particular, we intend to prove the existence (or nonexistence) of limit cycles for these classes of quadratic and cubic systems, which is a question related to the Hilbert 16 Problem. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
LLIBRE, JAUME; MESSIAS, MARCELO; REINOL, ALISSON DE CARVALHO. Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 25, n. 1, . (12/18413-7, 13/01743-7)
LLIBRE, JAUME; MESSIAS, MARCELO; REINOL, ALISSON C.. Darboux invariants for planar polynomial differential systems having an invariant conic. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 65, n. 6, p. 1127-1136, . (12/18413-7, 13/01743-7)

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