Periodic points of Hamiltonian surface diffeomorphisms

Abstract

The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S2 provided the diffeomorphism has at least three fixed points. In addition we show that up to isotopy relative to its fixed point set, every orientation preserving di eomorphism F: S→S of a closed orientable surface has a normal form. If the fixed point set is finite this is just the Thurston normal form.