Formas normais e ações de grupos no estudo de sistemas Hamiltonianos

• Ano de defesa: 2018
• Autor(a) principal: Jéssica Buzatto Prudencio
• Tipo de documento: Dissertação
• 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: Formas normais; Sistemas Hamiltonianos; Invariantes; Grupos de Lie lineares; Geometria simplética; Normal forms; Hamiltonian systems; Invariants; Linear Lie groups; Symplectic geometry; Ciências Exatas e da Terra; Matemática
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/5490

The central goal of this work is the development of the normal forms theory for Hamiltonians defined in a finite-dimensional symplectic vector space. To achieve this, we develop the adjoint operator method and an alternative algebraic method which takes into account a given group S of matrices in terms of the linear part of the associated Hamiltonian system. In this process, we use tools from the representation theory and invariant theory of linear Lie groups, as well as from the symplectic geometry. We exemplify the methods by obtaining normal forms of specific Hamiltonians, even under the action of a linear Lie group. In this last case, the normal form can inherit the symmetries of the original Hamiltonian, implying that the symmetries of the associated Hamiltonian field are also preserved