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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 1(5), Pages 3–17 (Mi msb3179)  

This article is cited in 4 scientific papers (total in 4 papers)

Regular components of homeomorphisms of the $n$-dimensional sphere

S. Kh. Aranson, V. S. Medvedev


Abstract: In this paper the structure of the regular components of homeomorphisms of the $n$-dimensional sphere is studied. Results are obtained which turn out to describe the possible types of regular components, and which generalize to dimensions $n\geqslant3$ the results of Birkhoff and Smith in dimension $2$. As applications we describe the regular components of structurally stable diffeomorphisms of $S^n$ with a finite number of periodic points and the connected components of orbitally stable trajectories of a structurally stable dynamical system on $S^n$ with a finite number of closed trajectories.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:1, 1–14

Bibliographic databases:

UDC: 513.83+517.9
MSC: Primary 57A15, 57D05; Secondary 54H20
Received: 03.02.1970 and 01.12.1970

Citation: S. Kh. Aranson, V. S. Medvedev, “Regular components of homeomorphisms of the $n$-dimensional sphere”, Mat. Sb. (N.S.), 85(127):1(5) (1971), 3–17; Math. USSR-Sb., 14:1 (1971), 1–14

Citation in format AMSBIB
\Bibitem{AraMed71}
\by S.~Kh.~Aranson, V.~S.~Medvedev
\paper Regular components of homeomorphisms of the $n$-dimensional sphere
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 1(5)
\pages 3--17
\mathnet{http://mi.mathnet.ru/msb3179}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=290347}
\zmath{https://zbmath.org/?q=an:0213.25501}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 1
\pages 1--14
\crossref{https://doi.org/10.1070/SM1971v014n01ABEH002601}


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    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. V. S. Medvedev, Ya. L. Umanskii, “Regular components of homeomorphisms on $n$-dimensional manifolds”, Math. USSR-Izv., 8:6 (1974), 1305–1322  mathnet  crossref  mathscinet  zmath
    2. S. Kh. Aranson, V. Z. Grines, “The topological classification of cascades on closed two-dimensional manifolds”, Russian Math. Surveys, 45:1 (1990), 1–35  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. E. V. Zhuzhoma, V. S. Medvedev, “Global Dynamics of Morse–Smale Systems”, Proc. Steklov Inst. Math., 261 (2008), 112–135  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. V. Z. Grines, E. V. Zhuzhoma, O. V. Pochinka, “Sistemy Morsa–Smeila i topologicheskaya struktura nesuschikh mnogoobrazii”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 61, RUDN, M., 2016, 5–40  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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