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arXiv · 2007.01741

Fixed points and the inverse problem for central configurations

D. L. Ferrario
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Abstract

Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed points of self-maps defined on the shape space, and some results on the inverse problem in dimension $1$, i.e. finding (positive or real) masses which make a given collinear configuration central. This survey article introduces readers to the recent results of the author, also unpublished, showing an application of the fixed point theory.

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D. L. Ferrario. 2020-07-03. Fixed points and the inverse problem for central configurations. https://arxiv.org/abs/2007.01741

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