Saari's Conjecture is True for Generic Vector Fields
| dc.creator | Schmah, Tanya | |
| dc.creator | Stoica, Cristina | |
| dc.date | 2005-10-01 | |
| dc.date.accessioned | 2026-07-07T06:20:33Z | |
| dc.date.available | 2026-07-07T06:20:33Z | |
| dc.description | The simplest non-collision solutions of the N-body problem are the "relative equilibria", in which each body follows a circular orbit around the centre of mass and the shape formed by the N bodies is constant. It is easy to see that the moment of inertia of such a solution is constant. In 1970, D. Saari conjectured that the converse is also true for the planar Newtonian N-body problem: relative equilibria are the only constant-inertia solutions. A computer-assisted proof for the 3-body case was recently given by R. Moeckel. We present a different kind of answer: proofs that several generalisations of Saari's conjecture are generically true. Our main tool is jet transversality, including a new version suitable for the study of generic potential functions. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510012 | |
| dc.identifier | http://arxiv.org/abs/math/0510012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95350 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | MSC-class: 70F10 (Primary); 57N75, 37J05 (Secondary) | |
| dc.title | Saari's Conjecture is True for Generic Vector Fields | |
| dc.type | text |