LOW-DIMENSIONAL QUASIPERIODIC MOTION IN HAMILTONIAN SYSTEMS

A new method was recently introduced for detecting chaos and order in N degree of freedom Hamiltonian systems: It is called Generalized Alignment Index (GALI) and predicts rapidly and accurately if a certain orbit is chaotic or regular, by computing the volume of k unit deviation vectors as they follow the given orbit in the 2N −dimensional phase space. As is well known, regu- lar orbits of N degrees of freedom Hamiltonian systems lie, in general, on N dimensional tori. It does happen, however, in many cases of physical interest that these tori have dimensions much lower than N. In this paper, we derive the asymptotic behavior of the GALIk indices for the case of lower dimensional tori and apply our results to the famous Fermi Pasta Ulam lattice.