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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.
DOI:
https://doi.org/10.4213/mzm1506
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English version:
Mathematical Notes, 1997, 61:3, 265–271
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UDC:
517.917+513.9
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
Citation in format AMSBIB
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\pages 323--331
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http://mi.mathnet.ru/eng/mz1506https://doi.org/10.4213/mzm1506 http://mi.mathnet.ru/eng/mz/v61/i3/p323
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This publication is cited in the following articles:
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E. V. Zhuzhoma, V. S. Medvedev, “The Closure Lemma for Piecewise Diffeomorphic Maps of the Circle”, Math. Notes, 69:2 (2001), 277–280
  -
Anosov D.V., Zhuzhoma E.V., “Closing Lemmas”, Differ. Equ., 48:13 (2012), 1653–1699
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