  In the hyperspace of subcontinua of a compact surface we consider a second
order Hausdorff distance. This metric space is compactified in such a way that
the stable foliation of a pseudo-Anosov map is naturally identified with a
hypercontinuum. We show that negative iterates of a stable arc converges to
this hypercontinuum in the considered metric. Some dynamical properties of
pseudo-Anosov maps, as topological mixing and the density of stable leaves, are
generalized for cw-expansive homeomorphisms of pseudo-Anosov type on compact
metric spaces.
