Qualitative theory of ordinary differential equations and applications to Economy

• Grant number: 24/08665-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2024
• End date: February 06, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Rafael Ribeiro dos Santos
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 22/02819-6 - Intermittent vector fields: theoretical aspects and applications, AP.PNGP.PI

Abstract

In this project we will have the scientific initiation article [CarLei] as the base text. In the theoretical part, we will study the Grobman-Hartmann Theorem, how to obtain phase portraitsof smooth vector fields (based on eigenvalues or eigenvectors), among others.In terms of applications in Economics, we will study the models: Palomba, ContinuousOligopoly, Continuous IS-LM, Tobin-Blanchard and Simple Inflation