Estabilidade de Lyapunov em fibrados

• Ano de defesa: 2016
• Autor(a) principal: Victor Hugo Lourenço da Rocha
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Brasil; Departamento de Matemática; Programa de Pós-Graduação em Matemática; UEM; Maringá, PR; Centro de Ciências Exatas
• Palavras-chave em Português: Estabilidade de Lyapunov; Atatores; Semigrupos (Topologia); Homomorfismo - Ações de semigrupos; Fibrados; Lyapunov stability; Attractors; Semigroups; Semigroups actions; Fiber bundles; Ciências Exatas e da Terra; Matemática
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/5531

In this work, we present some results on Lyapunov stability for semigroup actions on principal and associated bundles. We introduce the concept of orbit preserving map and study the behavior of stable sets and attractors under such maps. We use the results obtained for orbit preserving maps to study stable sets and attractors in the setting of principal and associated bundles. In addition, we present some result that relate stable sets and attractors in the total space of an associated bundle to the corresponding concepts in the fibers. Finally, we relate the concepts of stable sets and attractors for the zero section of a vector bundle in the context of n-time semiflows and control systems