Local and global aspects of the qualitative theory of ordinary differential equations

• Grant number: 17/25021-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2018
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Paulo Henrique Reis Santana
• 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
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

The project aims to introduce the student to the Qualitative Theory of Ordinary Differential Equations. In a first phase aspects of the local theory will be approached through the study of some classic results such as: existence and uniqueness theorem, theorems of dependence with respect to initial conditions and parameters, flow defined by a differential equation, the Grobman-Hartman theorem. In the final phase of the project, aspects of the global ODE theory such as limit and attractor sets, alpha- and omega-limit, Poincaré-Bendixon theorem, Poincaré's first return map in planar systems, Liapunov coefficients of a weak focus with the help of software MATHEMATICA. And to conclude the project we will study the number of limit cycles that bifurcate from the linear center by a perturbation of degree n. (AU)