Formas normais de sistemas hamiltonianos reversíveis equivariantes

Abstract

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.