Freedom in Small Parameter Expansion for Nonlinear Perturbations

Peter B. Kahn, Diana Murray, Yair Zarmi

Research output: Contribution to journalArticlepeer-review


The freedom of choice of the zero-order term in the perturbative analysis of harmonic oscillators that are perturbed by a nonlinear perturbation is investigated in detail within the framework of the method of normal forms in the case of the unforced Duffing oscillator. It is demonstrated that the choice leading to minimal normal forms (MNF) is by far the best, indicating that MNF may be a way to significantly improve the convergence properties of the perturbation series relative to the traditional expansions.
Original languageEnglish
Pages (from-to)83-94
JournalProceedings: Mathematical and Physical Sciences
Issue number1917
StatePublished - 1 Oct 1993


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