Teoria do Averaging para campos de vetores suaves por partes

• Ano de defesa: 2016
• Autor(a) principal: Velter, Mariana Queiroz
• Orientador(a): Tonon, Durval José
• Banca de defesa: Tonon, Durval José, Medrado, João Carlos da Rocha, Buzzi, Claudio Aguinaldo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Matemática (IME)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Ciclos limite; Teoria do Averaging; Campos de vetores suave por partes
• Palavras-chave em Inglês: Limit cycles; Averaging theory; Piecewise smooth vector fields
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/5568

In this work the first-order Averaging theory will be studied. This theory replaces the problem of finding and quantifying limit cycles of a vector field by the problem of finding positive zeros of a function. We present the classical Averaging method (done for C 2 smooth vector fields) and we apply it to some special cases of quadratic polynomial vector fields in R3. Afterwards, we show a generalization of the Averaging method proposed in [3], which uses Brouwer degree theory in order to extend the method to continuous vector field, in other words, the differentiability of a vector field is no longer required. Finally, we will study the Averaging theory for piecewise smooth vector fields, presented in [14] using the regularization technique for piecewise smooth vector fields, see [22]. Also we will apply it to a class of polynomial vector field defined by parts, known as Kukles fields, see [16].