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Introduction to the qualitative theory of ordinary differential equations

Grant number: 23/12320-1
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): October 01, 2023
Effective date (End): September 30, 2024
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


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.

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