  We study finite-time mixing in time-periodic open flow systems. We describe
the transport of densities in terms of a transfer operator, which is
represented by the transition matrix of a finite-state Markov chain. The
transport processes in the open system are organized by the chaotic saddle and
its stable and unstable manifolds. We extract these structures directly from
leading eigenvectors of the transition matrix. We use different measures to
quantify the degree of mixing and show that they give consistent results in
parameter studies of two model systems.
