Periodic orbits of the generalized Friedmann-Robertson-Walker Hamiltonian systems

The averaging theory of first order is applied to study a generalization of the Friedmann-Robertson-Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. © 2012 Springer Science+Business Media Dordrecht.