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Mat. Sb., 1994, Volume 185, Number 6, Pages 3–50 (Mi msb901)  

This article is cited in 16 scientific papers (total in 16 papers)

Hyperbolic attractors of diffeomorphisms of orientable surfaces

A. Yu. Zhirov

Gagarin Air Force Academy

Abstract: A method is proposed for describing combinatorially the one-dimensional hyperbolic attractors of diffeomorphisms of orientable surfaces and the corresponding pseudo-Anosov diffeomorphisms. Using this method a new invariant of topological conjugacy is introduced. The set of values of this invariant admits an effective enumeration.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:1, 135–174

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 58F12, 58F15; Secondary 57N05, 54F15, 57R65
Received: 27.04.1993

Citation: A. Yu. Zhirov, “Hyperbolic attractors of diffeomorphisms of orientable surfaces”, Mat. Sb., 185:6 (1994), 3–50; Russian Acad. Sci. Sb. Math., 82:1 (1995), 135–174

Citation in format AMSBIB
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\by A.~Yu.~Zhirov
\paper Hyperbolic attractors of diffeomorphisms of orientable surfaces
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 6
\pages 3--50
\mathnet{http://mi.mathnet.ru/msb901}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1280395}
\zmath{https://zbmath.org/?q=an:0854.58029}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 1
\pages 135--174
\crossref{https://doi.org/10.1070/SM1995v082n01ABEH003556}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RR54800007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Zhirov, “Hyperbolic attractors of diffeomorphisms of orientable surfaces”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 23–65  mathnet  crossref  mathscinet  zmath  isi
    2. A. Yu. Zhirov, “Hyperbolic attractors of diffeomorphisms of orientable surfaces. Part 3. Classification algorithm”, Sb. Math., 186:2 (1995), 221–244  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. A. Yu. Zhirov, “Solenoidal representations and the homology of hyperbolic attractors of diffeomorphisms of surfaces”, Sb. Math., 188:6 (1997), 799–821  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. A. Yu. Zhirov, “Examples of one-dimensional hyperbolic attractors on nonorientable surfaces”, Math. Notes, 65:3 (1999), 390–393  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. 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
    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. R. V. Plykin, “On the problem of topological classification of strange attractors of dynamical systems”, Russian Math. Surveys, 57:6 (2002), 1163–1205  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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. A. Yu. Zhirov, “Combinatorics of One-Dimensional Hyperbolic Attractors of Diffeomorphisms of Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 132–200  mathnet  mathscinet  zmath
    11. 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
    12. 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
    13. 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
    14. S. P. Kuznetsov, “Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics”, Phys. Usp., 54:2 (2011), 119–144  mathnet  crossref  crossref  adsnasa  isi  elib
    15. V. Z. Grines, E. D. Kurenkov, “Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets”, Izv. Math., 84:5 (2020), 862–909  mathnet  crossref  crossref  mathscinet  isi  elib
    16. V. Z. Grines, E. V. Zhuzhoma, E. D. Kurenkov, “On $DA$-endomorphisms of the two-dimensional torus”, Sb. Math., 212:5 (2021), 698–725  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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