  We prove that a generic area-preserving diffeomorphism of a compact surface
with non-empty boundary has an equidistributed set of periodic orbits. This
implies that such a diffeomorphism has a dense set of periodic points, although
we also give a self-contained proof of this "generic density'' theorem. One
application of our results is the extension of mean action inequalities proved
by Hutchings and Weiler for the disk and annulus to generic Hamiltonian
diffeomorphisms of any compact surface with boundary.
