From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition
Exactly Solvable and Integrable Systems
2009-10-31 v3 Dynamical Systems
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.
Cite
@article{arxiv.nlin/0005027,
title = {From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition},
author = {Yoshio Uwano},
journal= {arXiv preprint arXiv:nlin/0005027},
year = {2009}
}
Comments
23 pages, LaTeX (iop.sty), typos and Appendix added