Spiderweb central configurations
Olivier H\'enot, Christiane Rousseau

TL;DR
This paper investigates the existence and uniqueness of spiderweb central configurations in the N-body problem, providing constructive proofs, algorithms, and numerical insights into mass distributions.
Contribution
It offers constructive proofs and algorithms for the existence and uniqueness of spiderweb central configurations, with numerical simulations revealing properties of mass distribution.
Findings
Existence of spiderweb configurations proven constructively.
Uniqueness established for certain parameter ranges.
Numerical simulations show properties of mass distribution.
Abstract
In this paper we study spiderweb central configurations for the -body problem, i.e configurations given by masses located at the intersection points of concurrent equidistributed half-lines with circles and a central mass , under the hypothesis that the masses on the -th circle are equal to a positive constant ; we allow the particular case . We focus on constructive proofs of the existence of spiderweb central configurations, which allow numerical implementation. Additionally, we prove the uniqueness of such central configurations when and arbitrary and ; under the constraint we also prove uniqueness for and not too large. We also give an algorithm providing a rigorous proof of the existence and local unicity of such central…
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