On the number of noncontractible periodic orbits in Hamiltonian dynamics

Abstract In this paper, we treat noncontractible periodic orbits in Hamiltonian dynamics on symplectic manifolds. We prove that any Hamiltonian diffeomorphism has infinitely many simple noncontractible periodic orbits, provided that the Hamiltonian diffeomorphism has at least one periodic orbit of infinite order in the first homology group and the orbit has nontrivial local Floer cohomology. Our proof is an application of the equivariant Hamiltonian Floer cohomology.