Minimal normal forms in harmonic oscillations with small nonlinear perturbations

Peter B. Kahn; Yair Zarmi

doi:10.1016/0167-2789(91)90108-L

Minimal normal forms in harmonic oscillations with small nonlinear perturbations

Peter B. Kahn
, Yair Zarmi

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The freedom of choice of the zeroth-order approximation in the perturbative expansion of solutions to oscillatory problems with small nonlinearities is exploited within the framework of the method of normal forms. A priori, the normal form may contain an infinite number of resonant terms. It is shown that in a large class of problems of interest, the normal form can be simplified so that the number of such terms is small, or to have other desired properties. Conservative as well as dissipative systems are discussed.

Original language	English
Pages (from-to)	65-74
Number of pages	10
Journal	Physica D: Nonlinear Phenomena
Volume	54
Issue number	1-2
DOIs	https://doi.org/10.1016/0167-2789(91)90108-L
State	Published - 1 Jan 1991

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(91)90108-L

Cite this

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title = "Minimal normal forms in harmonic oscillations with small nonlinear perturbations",

abstract = "The freedom of choice of the zeroth-order approximation in the perturbative expansion of solutions to oscillatory problems with small nonlinearities is exploited within the framework of the method of normal forms. A priori, the normal form may contain an infinite number of resonant terms. It is shown that in a large class of problems of interest, the normal form can be simplified so that the number of such terms is small, or to have other desired properties. Conservative as well as dissipative systems are discussed.",

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AB - The freedom of choice of the zeroth-order approximation in the perturbative expansion of solutions to oscillatory problems with small nonlinearities is exploited within the framework of the method of normal forms. A priori, the normal form may contain an infinite number of resonant terms. It is shown that in a large class of problems of interest, the normal form can be simplified so that the number of such terms is small, or to have other desired properties. Conservative as well as dissipative systems are discussed.

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U2 - 10.1016/0167-2789(91)90108-L

DO - 10.1016/0167-2789(91)90108-L

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JO - Physica D: Nonlinear Phenomena

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Minimal normal forms in harmonic oscillations with small nonlinear perturbations

Abstract

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