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 Ū 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.
Ferrario, D. (2017). Central configurations, Morse and fixed point indices. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN, 24(4), 631-640 [10.36045/bbms/1515035012].
Central configurations, Morse and fixed point indices
Ferrario, DL
2017
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 Ū 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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