An introduction to the ordinary diferential equations qualitative theory

• Grant number: 12/11333-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2012
• Effective date (End): December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Daniele Alessandra Reghini Gazetta
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

We will use the study ever conducted by the candidate in linear algebra and application of the Jordan Canonical Form to describe the solutions of systems of linear ordinary differential equations to study qualitatively/geometrically nonlinear systems addressing the Existence and Uniqueness Theorem, Theorem Flow tubular, and Grobman-Hartman Theorem and some aspects of the global theory such as the Poincaré-Bendixson Theorem. Finally, we study the structural stability of vector fields in the plane via Peixoto Theorem and analyze in detail the bifurcations of non-hyperbolic equilibrium points and non-hyperbolic limit cycles.(AU)