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

Abstract

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)

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, JAN 2015. (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, DEC 2014. (12/18413-7, 13/01743-7)