An introduction to the ordinary differential equations qualitative theory

• Grant number: 11/24011-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2012
• End date: August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Lucas Kenjy Bazaglia Kuroda
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

We will begin the project with the study and application of canonical Jordan Form to describe the solutions of systems of linear ordinary differential equations. So we will study classical theorems such as the Theorem of Existence and uniqueness, the Tubular Flow theorem, Grobman-Hartman Theorem, and the Poincaré-Bendixson Theorem. Finally, we study the definition of structural stability of vector fields in R2 and the famous Peixoto theorem.(AU)