Introduction to qualitative theory of dynamical systems

• Grant number: 07/06641-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2008
• End date: December 31, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Rodrigo Donizete Euzébio
• 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

Abstract

First of all, we study the non-linear dynamical systems looking at the local perspective: Existence and Uniqueness Theorem, Grobman-Hartman Theorem, and Stable Manifold Theorem. After that, we study some aspects of the global dynamics as for example Poincaré-Bendixon Theorem. Finally, we study the Normal Form Theory: Poincaré theorem and Siegel theorem. (AU)