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

Abstract

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.

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.