Central configurations play an important role in the dynamics of the n-body problem, and have been studied as relative equilibria, critical points, or projective fixed points of maps on configuration spaces. We describe some results on central configuration as fixed points of quotient maps, and then on the inverse problem in dimension 1, i.e. finding (positive or real) masses which make a given collinear configuration central. We study the inverse problem as a fixed point problem for multi-valued maps.
Ferrario, D. (2020). Multi-Valued Fixed Points and the Inverse Problem for Central Configurations. Intervento presentato a: New Trends in Celestial Mechanics 2019, Cogne, Italy.
Multi-Valued Fixed Points and the Inverse Problem for Central Configurations
Ferrario, DL
2020
Abstract
Central configurations play an important role in the dynamics of the n-body problem, and have been studied as relative equilibria, critical points, or projective fixed points of maps on configuration spaces. We describe some results on central configuration as fixed points of quotient maps, and then on the inverse problem in dimension 1, i.e. finding (positive or real) masses which make a given collinear configuration central. We study the inverse problem as a fixed point problem for multi-valued maps.
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