|Support type:||Scholarships in Brazil - Scientific Initiation|
|Effective date (Start):||May 01, 2020|
|Effective date (End):||December 31, 2020|
|Field of knowledge:||Physical Sciences and Mathematics - Mathematics - Geometry and Topology|
|Principal researcher:||Pedro Toniol Cardin|
|Grantee:||Murilo de Souza Penteado|
|Home Institution:||Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil|
In this project, we will make an introductory study of the so-called smooth piecewise dynamical systems (or Filippov systems), which are systems of ordinary differential equations whose vector field does not have smoothness properties. We will study several mathematical concepts and ideas involving such systems, for example, the definition of local trajectory, the sliding vector field (or Filippov field), typical singularities, topological equivalence, periodic orbits, separatrices and the well-known regularization method. In addition, returning to the theory of smooth systems, we will study the concept of structural stability and Peixoto's theorem, as well as the simplest types of bifurcations that can occur in one-parameter families of smooth vector fields.