Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations

We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the past there exists a singularity. We identify and describe all possible past asymptotic states; in particular, on the past attractor set we establish the existence of a heteroclinic network, which is a new type of feature in general relativity. This illustrates among other things that Vlasov matter can lead to quite different dynamics of cosmological models as compared to perfect fluids.