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Assuming that the space-time is close to special solutions which will play the role of the ω-limit and that the maximal velocity of the particles is small, we have been able to show that for reflection symmetric Bianchi II and reflection symmetric Bianchi VI0 spacetimes with collisionless matter the asymptotic behaviour at late times is close to the special case of dust. The key was a bootstrap argument

Future non-linear stability of the Einstein-Vlasov system with reflection Bianchi II and VI0 symmetry