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
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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Mathematics of the USSR-Sbornik, 1971, 14:1, 1–14
MSC: Primary 57A15, 57D05; Secondary 54H20
Received: 03.02.1970 and 01.12.1970
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
\by S.~Kh.~Aranson, V.~S.~Medvedev
\paper Regular components of homeomorphisms of the $n$-dimensional sphere
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
V. S. Medvedev, Ya. L. Umanskii, “Regular components of homeomorphisms on $n$-dimensional manifolds”, Math. USSR-Izv., 8:6 (1974), 1305–1322
S. Kh. Aranson, V. Z. Grines, “The topological classification of cascades on closed two-dimensional manifolds”, Russian Math. Surveys, 45:1 (1990), 1–35
E. V. Zhuzhoma, V. S. Medvedev, “Global Dynamics of Morse–Smale Systems”, Proc. Steklov Inst. Math., 261 (2008), 112–135
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
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