Estudo qualitativo de campos suaves por partes via problema de perturbação singular

• Autor(a) principal: Santos, Mayk Joaquim dos
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000f54m
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6852
• topic: Campos de vetores suaves por partes; Problema de perturbação singular; Campo de Filippov; Bifurcação; Regularização; Piecewise smooth vector field; Singular perturbation problem; Filippov vector field; Bifurcation; Regularization; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we will show that, given a piecewise smooth vector field, we can apply the regularization method and, from it, via blow-up, turn it into a singular perturbation problem. By doing that, we can use the tools from singular perturbation theory to perform a qualitative study of piecewise smooth vector fields. Finally, we will show that, through successive changes of coordinates, a singularity of a discontinuous submanifold of codimension k, where k=1 or k=2, can be transformed into a singularity of codimension 0 in order to study the qualitative behavior in this submanifold, where the Filippov’s convention holds.