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 $H_{\epsilon }=H_0+\epsilon H_1+\frac{{\epsilon }^2}{2}{H}_2$, 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 Hénon-Heiles and the elastic pendulum Hamiltonians.

Third version. A more detailed mathematical treatment, the computational part has been relegated to the documentation of the package, which can be downloaded from http://galia.fc.uaslp.mx/~jvallejo/pdynamics.zip

References in corpus (1)

• Homological Equation for Tensor Field and Periodic Averaging

Cited by in corpus (2)

• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
• Hamiltonian systems: symbolical, numerical and graphical study