Singularities in Non-Smooth Dynamical Systems

• Grant number: 08/07337-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2009
• End date: June 30, 2009
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Ricardo da Silva
• Grantee: Rodrigo César Marini
• 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
• Associated research grant: 07/06896-5 - Geometry of control, dynamical and stochastic systems, AP.TEM

Abstract

We will describe some qualitative and geometricaspects of non-smooth dynamical systems theory around typical singularities. We will establish a interaction between non-smooth systems and the geometric singular perturbation theory. Such systems are represented by discontinuous vector fields where its discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring out some results that bridge the space between discontinuous systems and singularly perturbed smooth systems.