Estudo de conjuntos minimais para sistemas descontínuos em dimensões 2 e 3

• Ano de defesa: 2014
• Autor(a) principal: Euzébio, Rodrigo Donizete [UNESP]
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática; Sistemas dinâmicos diferenciais; Ciclo limite; Comportamento caótico nos sistemas; Poincaré-Bendixson, Teorema de
• Link de acesso: http://hdl.handle.net/11449/110601

In this thesis minimal sets of smooth and non-smooth vector fields in dimension 2 and 3 are studied. First the study of minimal sets is restricted to limit cycles. Questions about existence, distribution and quantity of such objects in smooth and non-smooth vector fields in dimension 3 are answered. Later, the existence of non-trivial minimal sets and chaos in dimension 2 is treated for non-smooth vector fields. Some examples of non-trivial minimal sets are presented and the presence of non-deterministic chaos on some of these sets is verified. Finally, a version of the Poincaré-Bendixson Theorem for non-smooth vector fields presenting neither escaping nor sliding motion is presented