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Planar dynamical systems with symmetries in space and time

Grant number: 11/19406-1
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): January 01, 2012
Effective date (End): June 30, 2012
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Míriam Garcia Manoel
Grantee:Gustavo Casagrande Oliveira
Home 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 anintroductoy and detailed study of these systems when they are defined from a system of differential equantions in the plane. A centralquestion in this direction regards the systematicstudy 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 ciences. It is through groups and group representation theory that we develop this setting in a systematic way,for this provides simplifications not only inthe computations but also in the analysis of theresults. It is in this context that the present project fits in, with the main aim to develop ina 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.