An introduction to the Qualitative Theory of Ordinary Differential Equations

• Grant number: 19/00028-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2019
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Isadora Zanato Leite
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

Throughout this project we will study the qualitative theory of Ordinary Differential Equations (ODEs). This study will be implemented through analysis of the phase portraits, which will provide us qualitative/geometric information’s regarding the dynamic behavior of such systems. Then we will deal with the formal results regarding the qualitative theory of vector fields including: The Existence and Uniqueness Theorem, the Flow Box Theorem, Grobman-Hartman's Theorem and The Poincaré-Bendixson's Theorem.