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Global analysis of Quadratic Planar Polynomial Vector Fields with Invariant Algebraic Surfaces

Grant number: 11/16154-1
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): March 01, 2012
Effective date (End): January 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Marcelo Messias
Grantee:Alisson de Carvalho Reinol
Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
Associated scholarship(s):13/01743-7 - Integrability of two-dimensional polynomial differential systems, BE.EP.MS


We propose the study of the main local and global techniques used in the analysis of planar polynomial vector fields: qualitative theory and bifurcation analysis (codimension 1 and 2); normal forms; desingularization techniques (blow-ups); Poincaré and Poincaré-Lyapunov compactification; drawn the global phase portrait of planar polynomial vector fields in the Poincaré sphere. We also propose the application of the techniques described above in the study of quadratic planar polynomial vector fields with an invariant algebraic curve and possible extensions of the results to cubic systems with invariant algebraic curves.

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
REINOL, Alisson de Carvalho. Análise global de sistemas quadráticos e cúbicos com duas circunferências não-concêntricas invariantes. 2014. Master's Dissertation - Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente Presidente Prudente.

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