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

Y. Uwano

2000年5月19日(金)15:15

3F南演習室

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization:
In 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 potential share the same BG-normal form up to degree-four, then both oscillators satisfy the Bertrand-Darboux integrability condition.

remark: The talk will be given in Japanese (^_^)