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Saari's Conjecture is True for Generic Vector Fields | | Tanya Schmah
; Cristina Stoica
; | | Date: |
1 Oct 2005 | | Subject: | Dynamical Systems; Differential Geometry; Geometric Topology MSC-class: MSC-class: 70F10 (Primary); 57N75, 37J05 (Secondary) | math.DS math.DG math.GT | | Abstract: | 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. | | Source: | arXiv, math.DS/0510012 | | Other source: | [GID 725976] math/0510012 | | Services: | Forum | Review | PDF | Favorites | |
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