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.
@article{MZM_1997_61_3_a0,
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/}
}
TY - JOUR AU - S. Kh. Aranson AU - E. V. Zhuzhoma AU - V. S. Medvedev TI - Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus JO - Matematičeskie zametki PY - 1997 SP - 323 EP - 331 VL - 61 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a0/ LA - ru ID - MZM_1997_61_3_a0 ER -
%0 Journal Article %A S. Kh. Aranson %A E. V. Zhuzhoma %A V. S. Medvedev %T Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus %J Matematičeskie zametki %D 1997 %P 323-331 %V 61 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a0/ %G ru %F MZM_1997_61_3_a0
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/