Periodic Orbits of Hamiltonian Systems Linear and Hyperbolic at Infinity
  We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have simple periodic orbits of arbitrarily large period when it has fixed points which are not necessary from a homological perspective. 
Basak Z. Gurel
math.SG math.DS