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arXiv · 1612.05937

Central configurations, Morse and fixed point indices

D. L. Ferrario
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Abstract

We compute the fixed point index of non-degenerate central configurations for the $n$-body problem in the euclidean space of dimension $d$, relating it to the Morse index of the gravitational potential function $\bar U$ induced on the manifold of all maximal $O(d)$-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.

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D. L. Ferrario. 2016-12-18. Central configurations, Morse and fixed point indices. https://arxiv.org/abs/1612.05937

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