Introduction to the qualitative theory of ordinary differential equations and applications

• Grant number: 22/10534-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2022
• End date: October 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Henrique Casellato Vitorio Rodrigues da Costa
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM

Abstract

We will start this project with the study of several examples modeled using ordinary differential equations. These examples will arise from electrical, biological, chemical and, mainly, mechanical problems. We will study these systems using their phase portraits, which will provide us important qualitative/geometric aspects regarding the behavior of such systems. Then we will deal with the formal results regarding the Qualitative Theory of Vector Fields, where we will addressclassic results such as: the Existence and Uniqueness Theorem, theTubular Flow Theorem, the Grobman-Hartman Theorem, and the Theoremof Poincaré-Bendixson.