# Stability of a point charge for the repulsive Vlasov-Poisson system

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We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small density with respect to Liouville measure (a cloud''), and we show that these solutions exist globally, that the electric field decays at an optimal rate and that the particle distribution converges along a modified scattering dynamics. This follows by a Lagrangian study of the linearized equation, which is integrated by means of an asymptotic action-angle coordinate transformation, and an Eulerian study of the nonlinear dynamic which exhibits the mixing'' mechanism responsible for the asymptotic behavior.