Avendaño Camacho, M.; Vallejo, J. A.; Vorobjev, Yu A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows. (English) Zbl 1352.70046 J. Phys. A, Math. Theor. 46, No. 39, Article ID 395201, 12 p. (2013). Summary: We study the determination of the second-order normal form for perturbed Hamiltonians \(H_{\varepsilon }=H_0 +\varepsilon H_1 +\frac{\varepsilon ^2}{2} H_2\), relative to the periodic flow of the unperturbed Hamiltonian \(H_0\). The formalism presented here is global, and can be easily implemented in any computer algebra system. We illustrate it by means of two examples: the Hénon-Heiles and the elastic pendulum Hamiltonians. Cited in 3 Documents MSC: 70H08 Nearly integrable Hamiltonian systems, KAM theory 70H05 Hamilton’s equations 70K45 Normal forms for nonlinear problems in mechanics 53D05 Symplectic manifolds (general theory) 53D17 Poisson manifolds; Poisson groupoids and algebroids 53D22 Canonical transformations in symplectic and contact geometry Keywords:second-order normal form for perturbed Hamiltonians; periodic flow of unperturbed Hamiltonian Software:Maxima PDFBibTeX XMLCite \textit{M. Avendaño Camacho} et al., J. Phys. A, Math. Theor. 46, No. 39, Article ID 395201, 12 p. (2013; Zbl 1352.70046) Full Text: arXiv