Periodic orbits of Hamiltonian homeomorphisms of surfaces

John Franks and Michael Handel [FH2] have recently proved that any nontrivial Hamiltonian diffeomorphism of a closed surface of genus at least one has periodic orbits of arbitrarily large period. They proved a similar result for a nontrivial area-preserving diffeomorphism of a sphere with at least three fired points. We emend these results to the case of the homeomorphisms. When the genus is at least one, we prove, moreover; that the periodic orbits may be chosen contractible if the set of contractible filed points is contained in a disk. When the surface is a sphere, we emend the result to the case of a nontrivial homeomorphism with no wandering points. The proofs make use of an equivariant foliated version of Brouwer's plane translation theorem (see [B, Proposition 2.1]) and some properties of the linking number of fired points.