Self-similarity breaking of cosmological solutions with collisionless matter

In this paper we consider the Einstein-Vlasov system with Bianchi VII$_0$ symmetry. Under the assumption of small data we show that self-similarity breaking occurs for reflection symmetric solutions. This generalizes the previous work concerning the non-tilted fluid case \cite{WHU} to the Vlasov case, and we obtain detailed information about the late-time behaviour of metric and matter terms.