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arXiv · 1301.3244

A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows

M. Avendaño-Camacho·J. A. Vallejo·Yu. Vorobjev
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Abstract

We study the determination of the second-order normal form for perturbed Hamiltonians $H_{\epsilon}=H_0 +\epsilon H_1 +\frac{\epsilon^2}{2} H_2$, 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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M. Avendaño-Camacho, J. A. Vallejo, Yu. Vorobjev. 2013-01-15. A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows. https://doi.org/10.1088/1751-8113/46/39/395201

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