0 From the Birkhoff - Gustavson normalization to the Bertrand - Darboux integrability condition † ‡ §
نویسنده
چکیده
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 oscillator with a homogeneous cubic-polynomial potential and the perturbed harmonic oscillator with a homogeneous quartic-polynomial potentials admit the same BG-normalization up to degree-4 then both oscillators satisfy the Bertrand-Darboux integrability condition.
منابع مشابه
From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition
The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the BirkhoffGustavson(BG)-normalization: In solving an inverse problem of the BGnormalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous cubic-polynomial potential and with a homogeneous quartic-polynomial potenti...
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