Generic equidistribution for area-preserving diffeomorphisms of compact surfaces with boundary

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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.