Introduction to the qualitative theory of ordinary differential equations

• Grant number: 23/12320-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2023
• End date: September 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luci Any Francisco Roberto
• Grantee: Pedro Henrique Freitas de Souza
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

This project aims to study basic notions and introductory results of Qualitative Theory of Ordinary Differential Equations. In particular, we concern to the existence and uniqueness of solutions, the $C^1$ dependence of solutions on the initial conditions, the Tubular Flow Theorem, the Hartman-Grobman Theorem, and differential equations in the plane with Poincaré-Bendixson Theory. We also give a brief introduction to bifurcation theory, center manifolds, normal forms, and Hamiltonian systems.