Fixed points and the inverse problem for central configurations
Copyright policy )Fixed points and the inverse problem for central configurations
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 This survey article introduces readers to the recent results of the author, also unpublished, showing an application of the fixed point theory.
Discriminantal varieties and configuration spaces in algebraic topology, \(n\)-body problem, Research exposition (monographs, survey articles) pertaining to algebraic topology, multi-valued map, Dynamical Systems (math.DS), Topological and differential topological methods for problems in mechanics, n body problem; multi-valued map; central configuration; inverse problem;, Fixed points and coincidences in algebraic topology, FOS: Mathematics, inverse problem, Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems, Mathematics - Dynamical Systems, central configuration, Central configuration; Inverse problem; Multi-valued map; N-body problem;
Discriminantal varieties and configuration spaces in algebraic topology, \(n\)-body problem, Research exposition (monographs, survey articles) pertaining to algebraic topology, multi-valued map, Dynamical Systems (math.DS), Topological and differential topological methods for problems in mechanics, n body problem; multi-valued map; central configuration; inverse problem;, Fixed points and coincidences in algebraic topology, FOS: Mathematics, inverse problem, Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems, Mathematics - Dynamical Systems, central configuration, Central configuration; Inverse problem; Multi-valued map; N-body problem;
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