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Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark

perturbed isotropic oscillators in four dimensions (or perturbed harmonic oscillators in 1:1:1:1 resonance). For those Hamiltonian systems, Sanders et al . [ 36 ] explain that the 1:...:1 resonance is one of the more complicated, due to large number of terms in the normal form. This proves to be a key issue in computations of higher order approximations, which is needed in bifurcation analysis for some values of the parameters. For this reason, any strategy developed to reduce the algebra involved in the normal form process, as well as in the subsequent analysis built on

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