  We study tilted perfect fluid cosmological models with a constant equation of
state parameter in spatially homogeneous models of Bianchi type VI$_{-1/9}$
using dynamical systems methods and numerical simulations. We study models with
and without vorticity, with an emphasis on their future asymptotic evolution.
We show that for models with vorticity there exists, in a small region of
parameter space, a closed curve acting as the attractor.
