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december 2017 Central configurations, Morse and fixed point indices
D.L. Ferrario
Bull. Belg. Math. Soc. Simon Stevin 24(4): 631-640 (december 2017). DOI: 10.36045/bbms/1515035012

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. "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

Information

Published: december 2017
First available in Project Euclid: 4 January 2018

zbMATH: 06848706
MathSciNet: MR3743267
Digital Object Identifier: 10.36045/bbms/1515035012

Subjects:
Primary: ‎55M20, 70F10

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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