Abstract
The freedon inherent in perturbative expansions is exploited within the framework of the method of normal forms, to demonstrate that the secular errors, evolving in approximations to solutions for harmonic oscillator systems with small nonlinear perturbations, can be reduced significantly by the minimal normal form (MNF) choice of the free resonant terms in the expansion. The MNF choice, previously developed for systems with one degree of freedom, is extended to higher-dimensional ones by applying it to the phase component of the normal form equations. The results are shown for a sequence of examples of growing complexity, starting with single oscillators and ending with three coupled oscillators.
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