Fixed points and the inverse problem for central configurations

2020/07/03 by Ferrario, D. L.
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.01741

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 This survey article introduces readers to the recent results of the author, also unpublished, showing an application of the fixed point theory.

Related

• Central configurations, symmetries and fixed points
• Central configurations of the curved N-body problem
• Central Configurations in the Trapezoidal Four-Body Problems
• The central configurations of four masses x, -x, y, -y
• Fixed point indices of central configurations