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Nonlinear ordinary differential equations: a first study

Grant number: 20/08906-2
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): September 01, 2020
Effective date (End): November 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Claudio Aguinaldo Buzzi
Grantee:Pedro Otávio de Souza Mussatto
Home 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:19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM

Abstract

The project aims to introduce the student to the Qualitative Theory of Ordinary Differential Equations. In a first phase, aspects of local theory will be addressed through the study of some classic results, such as: existence and uniqueness of solutions theorem, theorems of dependency in relation to initial conditions and parameters, flow defined by a differential equation, stable manifold theorem and the Grobman-Hartman theorem. In the final phase of the project, aspects of the global theory of ODE's will be addressed, such as: limit and attractor sets, alpha- and omega-limit, Poincaré-Bendixon theorem, first return Poincaré's map in planar systems, Lyapunov coefficients of a weak focus with the aid of an algebraic computing system. And to conclude the project we are going to study the number of limit cycles that bifurcate from the linear center by a n-degree perturbation.

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