Resumen de Spiderweb Central Configurations

Olivier Hénot, Christiane Rousseau

• In this paper we study spiderweb central configurations for the N-body problem, i.e configurations given by N=n×ℓ+1 masses located at the intersection points of ℓ concurrent equidistributed half-lines with n circles and a central mass m0, under the hypothesis that the ℓ masses on the i-th circle are equal to a positive constant mi; we allow the particular case m0=0. We focus on constructive proofs of the existence of spiderweb central configurations, which allow numerical implementations. Additionally, we prove by a rigorous numerical method the uniqueness of such central configurations when ℓ∈{2,…,9} and arbitrary n and mi; under the constraint m1≥m2≥⋯≥mn we also prove uniqueness for ℓ∈{10,…,18} and n not too large. We also give an algorithm providing a rigorous proof of the existence and local unicity of such central configurations when given as input a choice of n, ℓ and m0,…,mn. Finally, our numerical simulations highlight some interesting properties of the mass distribution.