Formas normais de sistemas hamiltonianos reversíveis equivariantes

• Ano de defesa: 2017
• Autor(a) principal: Priscila Friedemann Cardoso
• 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; Campos Hamiltonianos; Simetria; Antissimetria; Normal forms; Hamiltonian fields; Symetry; Ciências Exatas e da Terra; Matemática
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/5489

The main objective of this work is to determine formal normal forms of reversible- equivariant Hamiltonian vector fields under the action of a compact Lie group. For this, we present an algebric method derived from the classic method given by Belitskii [5,6] and Elphick et al. [13], which reduces this problem to computing the generators for the module of reversible equivariants by the action of a Lie group. In this process, we use tools from the invariant theory of groups and follow the approach given in [3]. We finish this work by applying the method in some specific examples of Z2-reversible-equivariant and D4−reversible-equivariant Hamiltonian vector fields with semisimple linearization and Zφ × Zψ-reversible-equivariant Hamiltonian vector fields with non-semisimple linearization, where φ e ψ are involutions acting as reversing symmetries.