Geodesic
Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus
Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 323-331

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We prove a strengthened $C^r$ -closing lemma ($r\ge1$) 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 ($r\ge1$) is proved for a special class of infinitely smooth actions of the integer lattice $\mathbb Z^k$ on the circle. The result is applied to foliations of codimension one with trivial holonomy group on the three-dimensional torus. 
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     author = {S. Kh. Aranson and E. V. Zhuzhoma and V. S. Medvedev},
     title = {Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--331},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a0/}
}
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S. Kh. Aranson; E. V. Zhuzhoma; V. S. Medvedev. Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus. Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 323-331. http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a0/