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

M. Avendaño-Camacho, J. A. Vallejo, Yu. Vorobjev

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 Hamiltoni…