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A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows (1301.3244v3)
Published 15 Jan 2013 in math-ph, math.DG, math.DS, math.MP, and nlin.SI
Abstract: We study the determination of the second-order normal form for perturbed Hamiltonians $H_{\epsilon}=H_0 +\epsilon H_1 +\frac{\epsilon2}{2} H_2$, relative to the periodic flow of the unperturbed Hamiltonian $H_0$. 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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