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 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 potential share the same BG-normal form up to degree-4, then both oscillators satisfy the Bertrand-Darboux integrability condition. AMS classification scheme numbers: 70K45, 70H06, 37J40, 37J40, 37K10 Short title: From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition February 8, 2008 2
منابع مشابه
0 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 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 hom...
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