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Mat. Sb. (N.S.), 1971, Volume 84(126), Number 2, Pages 301–312 (Mi msb3074)  

This article is cited in 24 scientific papers (total in 24 papers)

The topology of basis sets for Smale diffeomorphisms

R. V. Plykin

Abstract: Diffeomorphisms of a closed surface are considered which satisfy Smale's axiom $A$ and an acyclicity condition. It is shown that if one of its basis sets is one-dimensional, then there is also a zero-dimensional source or sink. As a preliminary, some auxiliary propositions of general character are established concerning sources and sinks of diffeomorphisms satisfying the axiom and the condition above.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 13:2, 297–307

Bibliographic databases:

UDC: 513.83
MSC: Primary 58F15; Secondary 28A65, 34C35, 54H20
Received: 11.04.1970

Citation: R. V. Plykin, “The topology of basis sets for Smale diffeomorphisms”, Mat. Sb. (N.S.), 84(126):2 (1971), 301–312; Math. USSR-Sb., 13:2 (1971), 297–307

Citation in format AMSBIB
\by R.~V.~Plykin
\paper The topology of basis sets for Smale diffeomorphisms
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 84(126)
\issue 2
\pages 301--312
\jour Math. USSR-Sb.
\yr 1971
\vol 13
\issue 2
\pages 297--307

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    This publication is cited in the following articles:
    1. V. Z. Grines, “O topologicheskoi ekvivalentnosti odnomernykh bazisnykh mnozhestv diffeomorfizmov na dvumernykh mnogoobraziyakh”, UMN, 29:6(180) (1974), 163–164  mathnet  mathscinet  zmath
    2. R. V. Plykin, “Sources and sinks of $A$-diffeomorphisms of surfaces”, Math. USSR-Sb., 23:2 (1974), 233–253  mathnet  crossref  mathscinet  zmath
    3. V. Z. Grines, E. V. Zhuzhoma, “The topological classification of orientable attractors on an $n$-dimensional torus”, Russian Math. Surveys, 34:4 (1979), 163–164  mathnet  crossref  mathscinet  zmath
    4. R. V. Plykin, “On the geometry of hyperbolic attractors of smooth cascades”, Russian Math. Surveys, 39:6 (1984), 85–131  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. V. Z. Grines, “On the topological classification of structurally stable diffeomorphisms of surfaces with one-dimensional attractors and repellers”, Sb. Math., 188:4 (1997), 537–569  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. Z. Grines, E. V. Zhuzhoma, “Structurally stable diffeomorphisms with basis sets of codimension one”, Izv. Math., 66:2 (2002), 223–284  mathnet  crossref  crossref  mathscinet  zmath
    8. D. V. Anosov, E. V. Zhuzhoma, “Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces”, Proc. Steklov Inst. Math., 238 (2002), 1–46  mathnet  mathscinet  zmath
    9. E. V. Zhuzhoma, V. S. Medvedev, “On non-orientable two-dimensional basic sets on 3-manifolds”, Sb. Math., 193:6 (2002), 869–888  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. E. V. Zhuzhoma, V. S. Medvedev, “On Typical Diffeotopy of Rough Diffeomorphisms with Expanding Attractor of Codimension One”, Math. Notes, 74:3 (2003), 453–456  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. Z. Grines, V. S. Medvedev, E. V. Zhuzhoma, “On Surface Attractors and Repellers in 3-Manifolds”, Math. Notes, 78:6 (2005), 757–767  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. D. V. Anosov, E. V. Zhuzhoma, “Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings”, Proc. Steklov Inst. Math., 249 (2005), 1–221  mathnet  mathscinet  zmath
    13. Grines, V, “On structurally stable diffeomorphisms with codimension one expanding attractors”, Transactions of the American Mathematical Society, 357:2 (2005), 617  crossref  isi  elib
    14. Grines, VZ, “Expanding attractors”, Regular & Chaotic Dynamics, 11:2 (2006), 225  crossref  isi  elib
    15. E. V. Zhuzhoma, V. S. Medvedev, “Surface Basic Sets with Wildly Embedded Supporting Surfaces”, Math. Notes, 85:3 (2009), 353–365  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. E. V. Zhuzhoma, N. V. Isaenkova, “Classification of One-Dimensional Expanding Attractors”, Math. Notes, 86:3 (2009), 333–341  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. Grines V.Z., Levchenko Yu.A., “O topologicheskoi klassifikatsii diffeomorfizmov na 3-mnogoobraziyakh s poverkhnostnymi dvumernymi attraktorami i repellerami”, Doklady akademii nauk, 447:2 (2012), 127–127  elib
    18. V. Z. Grines, Yu. A. Levchenko, O. V. Pochinka, “O topologicheskoi klassifikatsii diffeomorfizmov na 3-mnogoobraziyakh s poverkhnostnymi dvumernymi attraktorami i repellerami”, Nelineinaya dinam., 10:1 (2014), 17–33  mathnet
    19. Vyacheslav Z. Grines, Yulia A. Levchenko, Vladislav S. Medvedev, Olga V. Pochinka, “On the Dynamical Coherence of Structurally Stable 3-diffeomorphisms”, Regul. Chaotic Dyn., 19:4 (2014), 506–512  mathnet  crossref  mathscinet  zmath
    20. V. Z. Grines, Yu. A. Levchenko, O. V. Pochinka, “Topological Classification of Structurally Stable 3-Diffeomorphisms with Two-Dimensional Basis Sets”, Math. Notes, 97:2 (2015), 304–306  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. V. Z. Grines, Ye. V. Zhuzhoma, O. V. Pochinka, “Rough diffeomorphisms with basic sets of codimension one”, Journal of Mathematical Sciences, 225:2 (2017), 195–219  mathnet  crossref
    22. V. Z. Grines, M. K. Noskova, O. V. Pochinka, “The construction of an energy function for three-dimensional cascades with a two-dimensional expanding attractor”, Trans. Moscow Math. Soc., 76:2 (2015), 237–249  mathnet  crossref  elib
    23. Grines V. Zhuzhoma E., “Around Anosov-Weil Theory”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, ed. Katok A. Pesin Y. Hertz F., Amer Mathematical Soc, 2017, 123–154  crossref  mathscinet  isi  scopus
    24. V. Z. Grines, E. D. Kurenkov, “O giperbolicheskikh attraktorakh i repellerakh endomorfizmov”, Nelineinaya dinam., 13:4 (2017), 557–571  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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