Abstract
We compute the fixed point index of non-degenerate central configurations for the -body problem in the euclidean space of dimension , relating it to the Morse index of the gravitational potential function induced on the manifold of all maximal -orbits. In order to do so, we analyze the geometry of maximal orbit type manifolds, and compute Morse indices with respect to the mass-metric bilinear form on configuration spaces.
Citation
D.L. Ferrario. "Central configurations, Morse and fixed point indices." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 631 - 640, december 2017. https://doi.org/10.36045/bbms/1515035012
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