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From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition

Yoshio Uwano
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Abstract

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous-{\it cubic} polynomial potential and with a homogeneous-{\it quartic} polynomial potentials admit the same BG-normalization up to degree-4 then both oscillators satisfy the Bertrand-Darboux integrability condition.

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Yoshio Uwano. 2000-08-08. From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition. https://doi.org/10.1088/0305-4470%2F33%2F37%2F315

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