On the crossing limit cycles for piecewise linear differential systems on the plane

• Ano de defesa: 2019
• Autor(a) principal: Ruiz, Jeidy Johana Jimenez
• Orientador(a): Medrado, João Carlos da Rocha
• Banca de defesa: Medrado, João Carlos da Rocha, Tonon, Durval José, Lima, Maurício Firmino Silva, Martins, Ricardo Miranda, Buzzi, Cláudio Aguinaldo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• 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: Sistemas diferencias suaves por partes; Ciclos limite costurantes; Centros diferencias lineares; Cônicas; Cúbicas
• Palavras-chave em Inglês: Piecewise linear differential systems; Crossing limit cycles; Linear differential centers; Conics; Cubic
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/10260

In this work we analyze the version of Hilbert’s 16th problem for piecewise linear differential systems in the plane for a particular case, more precisely in Chapter 2 we study on the maximum numbers of crossing limit cycles that can have the planar piecewise linear differential systems separated by a straight line S and formed by two linear differential systems X−;X+ which singularities are symmetrical with respect to the straight line of discontinuity S and they are on the straight line y = sx, s e R. In [24, 27] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles nevertheless in [20, 28] were studied planar discontinuous piecewise linear differential centers where the curve of discontinuity is not a straight line, and it was shown that the number of crossing limit cycles in these systems is non-zero. For this reason it is interesting to study the role which plays the shape of the discontinuity curve in the number of crossing limit cycles that planar discontinuous piecewise linear differential centers can have. In Chapter 3 we study on the upper bounds for the maximum number of crossing limit cycles with either two or four points on the discontinuity curve S, when S is any conic. And finally in Chapter 4 we study on the numbers of crossing limit cycles with four points on the discontinuity curve S, when S is a reducible cubic curve formed either by a circle and a straight line, or by a parabola and a straight line.