Conjuntos minimais de sistemas lineares por partes

• Ano de defesa: 2014
• Autor(a) principal: Moraes, Jaime Rezende de [UNESP]
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática; Equações diferenciais; Ciclo limite; Sistemas lineares; Differential equations
• Link de acesso: http://hdl.handle.net/11449/111008

The main goal of this thesis is to find periodic solutions of non–smooth systems. Our contribution in this thesis is related to the study of piecewise linear vector fields, singularly perturbed non–smooth systems and cubic polynomial differential systems in R2 with centers. We study piecewise linear planar vector fields (PWL). We suppose that the equilibrium points are saddle or focus. We establish a correspondence between the PWL vector fields and vectors formed by some of the following parameters: sets on (crossing, sliding or escaping), kind of equilibrium (real or virtual), intersection of the separatrices with , stability and orientation of the focus. Such vectors are called configurations. We reduce the number of the configurations by an equivalent relation and we analyze for which configurations the corresponding PWL vector fields can have or not closed sliding poly-trajectories. For the singularly perturbed non–smooth systems we study two classes of non–smooth singular perturbation problems: with one critical manifold and with two critical manifolds. For the first class we give sufficient conditions for the persistence of closed poly–trajectories. For the second class we give conditions for persistence of equilibrium points. For the cubic polynomial differential systems in R2 with centers we study the maximum number of limit cycles that bifurcate from some families of planar polynomial differential systems of degree 3 with rational first integrals of degree 2 when they are perturbed inside the classes of all cubic polynomial differential systems