New examples of conservative systems on S^2 possessing an integral cubic in momenta
| dc.creator | Selivanova, Elena N. | |
| dc.date | 1997-11-10 | |
| dc.date.accessioned | 2026-07-07T03:24:35Z | |
| dc.date.available | 2026-07-07T03:24:35Z | |
| dc.description | It has been proved that on 2-dimensional orientable compact manifolds of genus $g>1$ there is no integrable geodesic flow with an integral polynomial in momenta. There is a conjecture that all integrable geodesic flows on $T^2$ possess an integral quadratic in momenta. All geodesic flows on $S^2$ and $T^2$ possessing integrals linear and quadratic in momenta have been described by Kolokol'tsov, Babenko and Nekhoroshev. So far there has been known only one example of conservative system on $S^2$ possessing an integral cubic in momenta: the case of Goryachev-Chaplygin in the dynamics of a rigid body. The aim of this paper is to propose a new one-parameter family of examples of complete integrable conservative systems on $S^2$ possessing an integral cubic in momenta. We show that our family does not include the case of Goryachev-Chaplygin. | |
| dc.description | 10 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9711005 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9711005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33381 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.title | New examples of conservative systems on S^2 possessing an integral cubic in momenta | |
| dc.type | text |