Um estudo dos ciclos limites de campos suaves por partes no plano

• Autor(a) principal: Contreras, Jeferson Arley Poveda
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000dqgn
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/8268
• topic: Campos suaves por partes; Ciclos limite; Campos de Filippov; Função de Melnikov; Método do Averaging; Campos de vetores hamiltonianos; Piecewise smooth vector field; Limit cycles; Filippov vector fields; Melnikov function; Averaging method; Hamiltonian vector fields; GEOMETRIA E TOPOLOGIA::SISTEMAS DINAMICOS

The goal of this work is study limit cycles of piecewise smooth vector fields. First, we present the basic theory, passing through the areas of analysis, qualitative theory of differential equations and algebra. We also present basic concepts of Filippov fields, which are indispensable for the study of piecewise smooth fields. In chapter one, was the main topic, a general method for finding limit cycles will be described; in the second chapter limit cycles are found in a piecewise smooth vector field with non-degenerate center being perturbed by a piecewise polynomial vector field. In the fourth chapter, we study limit cycles in piecewise smooth Hamiltonian fields.