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It is shown that the generalized Collins--Stewart radiation and Milnesolutions are attractors of the massless Einstein--Vlasov system for Bianchitypes II and V spacetimes, respectively. The proof is based on an energy methodand bootstrap argument which are used to determine the decay rates of theperturbations away from the attractors.

Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter