  This paper contains two main results. The first is the existence of an
equivariant Weil-Petersson geodesic in Teichmueller space for any choice of
pseudo-Anosov mapping class. As a consequence one obtains a classification of
the elements of the mapping class group as Weil-Petersson isometries which is
parallel to the Thurston classification. The second result concerns the
asymptotic behavior of these geodesics. It is shown that geodesics that are
equivariant with respect to independent pseudo-Anosov's diverge. It follows
that subgroups of the mapping class group which contain independent
pseudo-Anosov's act in a reductive manner with respect to the Weil-Petersson
geometry. This implies an existence theorem for equivariant harmonic maps to
the metric completion.
