Dynamics of spatially homogeneous locally rotationally symmetric solutionsof the Einstein-Vlasov equations

The dynamics of the Einstein-Vlasov equations for a class of cosmological m odels with four Killing vectors is discussed in the case of massive particl es. It is shown that in all models analysed the solutions with massive part icles are asymptotic to solutions with massless particles at early times. I t is also shown that in Bianchi types I and II the solutions with massive p articles are asymptotic to dust solutions at late times. That Bianchi type III models are also asymptotic to dust solutions at late times is consisten t with our results but is not established by them.