  We continue our study of the dynamics of mappings with small topological
degree on (projective) complex surfaces. Previously, under mild hypotheses, we
have constructed an ergodic ``equilibrium'' measure for each such mapping. Here
we study the dynamical properties of this measure in detail: we give optimal
bounds for its Lyapunov exponents, prove that it has maximal entropy, and show
that it has product structure in the natural extension. Under a natural further
assumption, we show that saddle points are equidistributed towards this
measure. This generalize results that were known in the invertible case and is,
to our knowledge, one among not very many instances in which a natural
invariant measure for a non-invertible dynamical system is well-understood.
