Summary
Reduced dynamics obtained via the normal form style in the parametrisation method for invariant manifolds are analyzed for nonlinear vibratory systems. Thanks to symbolic and numerical asymptotic expansions, systematic developments allow one to show how the solutions are a generalization to arbitrary orders of the results obtained with perturbative approaches, in the more general context of efficient and direct reduction techniques. Illustrative examples on simple systems are shown, which can then be easily generalized to low-dimensional reduced dynamics obtained from large-scale models.
