Generalizations of Gordon theorem (Q1860551)

The Gordon theorem reads that if all trajectories of an autonomous Hamiltonian system are periodic and locally define a trivial foliation of the phase space then, in some neighborhood of any trajectory of the system, the period and the action function are the functions of the Hamiltonian only, see [\textit{B. W. Gordon}, J. Math. Mech. 19, 111-114 (1969; Zbl 0179.42004)]. The author generalizes this theorem for the case when some invariant submanifold of the phase space is foliated into isotropic invariant tori.