|
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
Full text:
PDF file (238 kB)
References:
PDF file
HTML file
English version:
Mathematical Notes, 1997, 61:3, 265–271
Bibliographic databases:
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
\Bibitem{AraZhuMed97}
\by S.~Kh.~Aranson, E.~V.~Zhuzhoma, V.~S.~Medvedev
\paper Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 3
\pages 323--331
\mathnet{http://mi.mathnet.ru/mz1506}
\crossref{https://doi.org/10.4213/mzm1506}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619735}
\zmath{https://zbmath.org/?q=an:0915.58090}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 3
\pages 265--271
\crossref{https://doi.org/10.1007/BF02355407}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997XR25700001}
Linking options:
http://mi.mathnet.ru/eng/mz1506https://doi.org/10.4213/mzm1506 http://mi.mathnet.ru/eng/mz/v61/i3/p323
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
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
|
Number of views: |
This page: | 233 | Full text: | 108 | References: | 56 | First page: | 1 |
|