Strengthening the C-tau-closing lemma for dynamical systems and foliations on the torus

We prove a strengthened C-r-closing lemma (r greater than or equal to 1) for wandering chain recurrent trajectories of flows without equilibrium states on the two-dimensional torus and for wandering chain recurrent orbits of a diffeomorphism of the circle. The strengthened C-r-closing lemma (r greater than or equal to 1) is proved for a special class of infinitely smooth actions of the integer lattice Z(k) on the circle. The result is applied to foliations of codimension one with trivial holonomy group on the three-dimensional torus.