A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows
Abstract
We study the determination of the second-order normal form for perturbed Hamiltonians Hε=H0 +ε H1 +ε22 H2, relative to the periodic flow of the unperturbed Hamiltonian H0. The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the H\'enon-Heiles and the elastic pendulum Hamiltonians.
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