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.
News published in Agência FAPESP Newsletter about the scholarship: