On the problem of stability for higher-order derivative Lagrangian systems

The problem of stability for dynamical systems whose Lagrangian function depends on the derivatives of a higher order than one is studied. The difficulty of this analysis arises from the indefiniteness of the Hamiltonian, so that the well-known Lagrange-Dirichlet theorem cannot be used and the methods of the canonical perturbation theory (KAM theory) must be employed. We show, with an example, that the indefiniteness of the energy does not forbid the stability.