Central configurations, Morse and fixed point indices

2016/12/18 by Davide L. Ferrario, Ferrario, D. L.
Mathematics · Physics and Astronomy · #55M20 #70F10 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1612.05937

openalex publication_date 2016/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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