Continuation of periodic orbits in conservative and Hamiltonian systems

We introduce and justify a computational scheme for the continuation of periodic orbits in systems with one or more first integrals, and in particular in Hamiltonian systems having several independent symmetries. Our method is based on a generalization of the concept of a normal periodic orbit as introduced by Sepulchre and MacKay [Nonlinearity 10 (1997) 679]. We illustrate the continuation method on some integrable Hamiltonian systems with two degrees of freedom and briefly discuss some further applications.