Periodic orbits of Hamiltonian systems: Applications to perturbed Kepler problems

We provide for a class of Hamiltonian systems in the action-angle variables sufficient conditions for showing the existence of periodic orbits. We expand this result to the study of the existence of periodic orbits of perturbed spatial Keplerian Hamiltonians with axial symmetry. Finally, we apply these general results for finding periodic orbits of the Matese-Whitman Hamiltonian, of the spatial anisotropic Hamiltonian and of the spatial generalized van der Waals Hamiltonian.