  When a birational surface map is expanding on cohomology there is a canonical
way to associate positive closed currents to the map and its inverse. In this
paper we use a version of Dirichlet energy to construct the wedge product of
these two currents under a very weak additional condition on the map. We show
that the resulting measure is invariant and mixing, and we establish that its
Lyapunov exponents are finite and non-zero.
