Os teoremas de Sturm e geometria simplética

• Ano de defesa: 2012
• Autor(a) principal: Vitor Luiz de Almeida
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Sistemas hamiltonianos; Grassmaninana lagrangiana; Índice de Marlov; Teoremas de Sturm; Matemática; Geometria simplética; Indice de Maslov; Funcoes de langranian
• Link de acesso: http://hdl.handle.net/1843/EABA-8YASAW

We studied systems of non-autonomous ordinary differential equations of the form (B(t)x0)0 = A(t)x, x E Rn, in which the matrices A(t) e B(t) are symmetric for all t in reals, identifying them with equivalent hamiltonian systems in R2n. We'd given topological and geometrical properties of Grassmanian Lagrangian A(n) and their trains. The transversal orientation of the minimal codimension train A1() allowed us to definethe Maslov's index. With help of the Symplectic Geometry and Algebraic Topology, we'd get generalizations of the Sturm classical theorems (comparison and separation theorems and their consequences) for n-dimensional case.