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Uspekhi Mat. Nauk, 1986, Volume 41, Issue 1(247), Pages 149–169 (Mi umn1972)  

This article is cited in 18 scientific papers (total in 18 papers)

Topological classification of flows on closed two-dimensional manifolds

S. Kh. Aranson, V. Z. Grines


Full text: PDF file (1606 kB)
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English version:
Russian Mathematical Surveys, 1986, 41:1, 183–208

Bibliographic databases:

UDC: 513.83+517.9
MSC: 37C15, 37D40, 37D15
Received: 28.01.1985

Citation: S. Kh. Aranson, V. Z. Grines, “Topological classification of flows on closed two-dimensional manifolds”, Uspekhi Mat. Nauk, 41:1(247) (1986), 149–169; Russian Math. Surveys, 41:1 (1986), 183–208

Citation in format AMSBIB
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\paper Topological classification of flows on closed two-dimensional manifolds
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\yr 1986
\vol 41
\issue 1(247)
\pages 149--169
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\transl
\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 1
\pages 183--208
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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. D. V. Anosov, “On the behavior in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces. I”, Math. USSR-Izv., 30:1 (1988), 15–38  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. S. Kh. Aranson, E. V. Zhuzhoma, “On the structure of quasiminimal sets of foliations on surfaces”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 397–424  mathnet  crossref  mathscinet  zmath  isi
    4. Philip Boyland, “Topological methods in surface dynamics”, Topology and its Applications, 58:3 (1994), 223  crossref
    5. 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
    6. James A. Walsh, “Directions for structurally stable flows on surfaces via rotation vectors”, Topology and its Applications, 66:1 (1995), 49  crossref
    7. V. Z. Grines, “Structural stability and asymptotic behavior of invariant manifolds ofA-diffeomorphisms of surfaces”, J Dyn Control Syst, 3:1 (1997), 91  crossref  mathscinet  zmath
    8. A. A. Oshemkov, V. V. Sharko, “Classification of Morse–Smale flows on two-dimensional manifolds”, Sb. Math., 189:8 (1998), 1205–1250  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. D. V. Anosov, “On the Lifts to the Plane of Semileaves of Foliations on the Torus with a Finite Number of Singularities”, Proc. Steklov Inst. Math., 224 (1999), 20–45  mathnet  mathscinet  zmath
    10. A. O. Prishlyak, “Morse–Smale Vector Fields without Closed Trajectories on 3-Manifolds”, Math. Notes, 71:2 (2002), 230–235  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. D. V. Anosov, “Flows on Closed Surfaces and Related Geometrical Questions”, Proc. Steklov Inst. Math., 236 (2002), 12–18  mathnet  mathscinet  zmath
    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. 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
    14. N. I. Zhukova, “Minimal Sets of Cartan Foliations”, Proc. Steklov Inst. Math., 256 (2007), 105–135  mathnet  crossref  mathscinet  zmath  elib  elib
    15. M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908  mathnet  crossref  mathscinet  zmath  elib  elib
    16. 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
    17. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
    18. David Angeli, Russell Johnson, “On detachable maps and flows”, Journal of Difference Equations and Applications, 2012, 1  crossref
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