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This article is cited in 2 scientific papers (total in 2 papers)
Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus
S. Kh. Aranson, E. V. Zhuzhoma, V. S. Medvedev Nizhnii Novgorod State Agricultural Academy
Abstract:
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.
Received: 03.10.1995
Citation:
S. Kh. Aranson, E. V. Zhuzhoma, V. S. Medvedev, “Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus”, Mat. Zametki, 61:3 (1997), 323–331; Math. Notes, 61:3 (1997), 265–271
Linking options:
https://www.mathnet.ru/eng/mzm1506https://doi.org/10.4213/mzm1506 https://www.mathnet.ru/eng/mzm/v61/i3/p323
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Abstract page: | 355 | Full-text PDF : | 176 | References: | 66 | First page: | 1 |
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