Planar dynamical systems with symmetries in space and time

• Grant number: 11/19406-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2012
• End date: June 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Míriam Garcia Manoel
• Grantee: Gustavo Casagrande Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 08/54222-6 - Singularities, geometry and differential equations, AP.TEM

Abstract

A dynamical system is one whose states change with time. This project intends to develop an introduction and detailed study of these systems when they are defined from a system of differential equations in the plane. A central question in this direction regards the systematic study of such systems in presence of symmetries. Since they are found in a great variety of models in the universe, the recognition of the occurrence of symmetries has a crucial role in Mathematics and other related sciences. It is through groups and group representation theory that we develop this setting in a systematic way, for this provides simplifications not only in the computations but also in the analysis of the results. It is in this context that the present project fits in, with the main aim to develop in solid form the group theory and its applications to the equivariant differential equations. For the applications, we propose a series of models to be treated.(AU)