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Introduction to the Planar Dynamical Systems

Grant number: 13/04532-7
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): May 01, 2013
Effective date (End): April 30, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Ricardo Miranda Martins
Grantee:Guilherme Tavares da Silva
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM

Abstract

The aim of this project is to introduce the Dynamical Systems theory to the student. We focus on the planar systems.We begin by a theoretical study, including important results like the Flow-Box Theorem, and theorems by Poincare-Bendixson and Hartman-Grobman.Then we consider some special classes of DS, namely reversible and conservative (Hamiltonian) vector fields.In this context, we study conditions under which a quadratic system admit a center.Finally we study the number of limit cycles that bifurcates from a center, using the Averaging Theory.