Índice de Conley para atratores de inclusão diferencial

• Ano de defesa: 2018
• Autor(a) principal: Queiroz, Lenison Alves de
• Orientador(a): Vieira, Ewerton Rocha
• Banca de defesa: Vieira, Ewerton Rocha, Euzébio, Rodrigo Donizete, Lima, Dahisy Valadão de Sousa
• 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: Equações diferenciais; Pontos de equilíbrio; Índice homológico; Índice de Conley; Índice de Morse
• Palavras-chave em Inglês: Differential equations; Equilibrium points; Homology index; Conley index; Morse index
• Área do conhecimento CNPq: GEOMETRIA E TOPOLOGIA::SISTEMAS DINAMICOS
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/8900

The present work deals with mathematical themes called Conley’s theory, differential inclu- sions and Morse theory inserted in this variant is the topological invariant for the region of discontinuity, the Conley index of discontinuous vector fields, where the discontinuities are concentrated on a surface. With this invariant it is possible to predict bifurcation results, as well as results of regularization of the discontinuous field. In Conley’s Theory, one doesn’t investigate only a single invariant set in a system; on the contrary, it is a decomposition of an invariant set into several “smaller” invariant subsets along with the orbits that connect these subsets. The methodology adopted for the research was based on the deductive analy- sis, a method that allowed the determination of the Conley index using tools of differential inclusions, index-pair and Morse theory to arrive at the determination of the homological in- dex.