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Uspekhi Mat. Nauk, 1990, Volume 45, Issue 1(271), Pages 3–32 (Mi umn4689)  

This article is cited in 14 scientific papers (total in 14 papers)

The topological classification of cascades on closed two-dimensional manifolds

S. Kh. Aransona, V. Z. Grinesb

a Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
b Nizhnii Novgorod State Agricultural Academy

Full text: PDF file (2421 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1990, 45:1, 1–35

Bibliographic databases:

UDC: 513.83+517.9
MSC: 57R50, 58K65, 54D10, 55Pxx, 57R30
Received: 29.01.1989

Citation: S. Kh. Aranson, V. Z. Grines, “The topological classification of cascades on closed two-dimensional manifolds”, Uspekhi Mat. Nauk, 45:1(271) (1990), 3–32; Russian Math. Surveys, 45:1 (1990), 1–35

Citation in format AMSBIB
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\by S.~Kh.~Aranson, V.~Z.~Grines
\paper The topological classification of cascades on closed two-dimensional manifolds
\jour Uspekhi Mat. Nauk
\yr 1990
\vol 45
\issue 1(271)
\pages 3--32
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\jour Russian Math. Surveys
\yr 1990
\vol 45
\issue 1
\pages 1--35
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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., 82:1 (1995), 135–174  mathnet  crossref  mathscinet  zmath  isi
    2. S. Kh. Aranson, V. Z. Grines, E. V. Zhuzhoma, “On the geometry and topology of flows and foliations on surfaces and the Anosov problem”, Sb. Math., 186:8 (1995), 1107–1146  mathnet  crossref  mathscinet  zmath  isi
    3. S. Kh. Aranson, R. V. Plykin, A. Yu. Zhirov, E. V. Zhuzhoma, “Exact upper bounds for the number of one-dimensional basic sets of surfaceA-diffeomorphisms”, J Dyn Control Syst, 3:1 (1997), 1  crossref  mathscinet  zmath
    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. 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
    6. Ch. Bonatti, V. Z. Grines, O. V. Pochinka, “Classification of Morse–Smale Diffeomorphisms with a Finite Set of Heteroclinic Orbits on 3-Manifolds”, Proc. Steklov Inst. Math., 250 (2005), 1–46  mathnet  mathscinet  zmath
    7. A. O. Prishlyak, “Complete topological invariants of Morse–Smale flows and handle decompositions of 3-manifolds”, J. Math. Sci., 144:5 (2007), 4492–4499  mathnet  crossref  mathscinet  zmath  elib
    8. Grines, VZ, “Expanding attractors”, Regular & Chaotic Dynamics, 11:2 (2006), 225  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. 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
    10. A. Yu. Zhirov, “How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?”, Math. Notes, 94:1 (2013), 96–106  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. V. Z. Grines, O. V. Pochinka, S. van Strien, “On $2$-diffeomorphisms with one-dimensional basic sets and a finite number of moduli”, Mosc. Math. J., 16:4 (2016), 727–749  mathnet  crossref  mathscinet
    12. Grines V.Z., Medvedev T.V., Pochinka O.V., “Dynamical Systems on 2-and 3-Manifolds Introduction”: Grines, VZ Medvedev, TV Pochinka, OV, Dynamical Systems on 2- and 3-Manifolds, Developments in Mathematics, 46, Springer International Publishing Ag, 2016, XVII–XXVI  isi
    13. 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
    14. 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
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