Saari's conjecture is true for generic vector fields

• Autores: Tanya Schmah, Cristina Stoica
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 9, 2007, págs. 4429-4448
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04330-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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, Trans. Amer. Math. Soc. (2005). 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.