Topics on Qualitative theory of ordinary differential equations

• Grant number: 24/03495-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2024
• End date: November 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Iago Guilherme Comin
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

This project aims to introduce the candidate to some significant outcomes of the Qualitative Theory of Ordinary Differential Equations (ODEs) and their applications. Among the results to be studied, we highlight the Theorems of Tubular Flow, Poincaré-Bendixson, and the Integrability Theory for systems defined in the plane.It is worth noting that the student has already explored crucial tools in a previous scientific initiation project, such as the Existence and Uniqueness Theorem for solutions, the classification of phase portraits of a planar system, and the Grobman-Hartman Theorem.