Formas normais e estabilidade de sistemas hamiltonianos degenerados

• Ano de defesa: 2015
• Autor(a) principal: Jesus, Robson Andrade de
• Orientador(a): Santos, Fábio dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Sergipe
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• País: BR
• Palavras-chave em Português: Estabilidade; Sistemas Hamiltonianos; Formas normais
• Palavras-chave em Inglês: Stability; Hamiltonian Systems; Normal form
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://ri.ufs.br/handle/riufs/6516

In this thesis we studied the theory of stability in equilibrium solutions of autonomous Hamiltonian systems with two degrees of freedom in degenerate cases. We specifically focusedour study on two cases, namely, when there are a first-order single resonance and a first-orderdouble resonance. After approaching standardization algorithms of the Hamiltonianquadratic part, the main technique used is to obtain the normal form of the Hamiltonian Lie up to a suitable order and,by using the theorem of Invariant Curve, we provided some conditions for stability of the new Hamiltonian coefficients. We studied the classical theorems of Chetaev, assuming that the origin of the phase space corresponds to the balance of that system. As an illustration, we resolved a partial reciprocal of Lagrange-Dirichlet theorem with two degrees of freedom, and made some comments regarding this reciprocal to one degree of freedom.