Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1997, Volume 61, Issue 3, Pages 323–331 (Mi mz1506)  

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/mz1506
  • https://doi.org/10.4213/mzm1506
  • http://mi.mathnet.ru/eng/mz/v61/i3/p323

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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:
    1. E. V. Zhuzhoma, V. S. Medvedev, “The Closure Lemma for Piecewise Diffeomorphic Maps of the Circle”, Math. Notes, 69:2 (2001), 277–280  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Anosov D.V., Zhuzhoma E.V., “Closing Lemmas”, Differ. Equ., 48:13 (2012), 1653–1699  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:251
    Full text:139
    References:56
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021