Introduction to the planar dynamical systems

• Grant number: 13/04532-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date until: May 01, 2013
• End date until: April 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Guilherme Tavares da Silva
• Host 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 with 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 admits a center. Finally, we study the number of limit cycles that bifurcate from a center, using the Averaging Theory. (AU)