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Mat. Zametki, 1993, Volume 54, Issue 3, Pages 3–17 (Mi mz2400)  

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

Topological classification of Morse–Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces

V. Z. Grines

Nizhnii Novgorod State Agricultural Academy

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English version:
Mathematical Notes, 1993, 54:3, 881–889

Bibliographic databases:

UDC: 517
Received: 24.12.1992

Citation: V. Z. Grines, “Topological classification of Morse–Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces”, Mat. Zametki, 54:3 (1993), 3–17; Math. Notes, 54:3 (1993), 881–889

Citation in format AMSBIB
\by V.~Z.~Grines
\paper Topological classification of Morse--Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces
\jour Mat. Zametki
\yr 1993
\vol 54
\issue 3
\pages 3--17
\jour Math. Notes
\yr 1993
\vol 54
\issue 3
\pages 881--889

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    This publication is cited in the following articles:
    1. V. Z. Grines, Kh. Kh. Kalai, “On the topological classification of gradient-like diffeomorphisms on irreducible three-dimensional manifolds”, Russian Math. Surveys, 49:2 (1994), 157–158  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. Z. Grines, “On the topological equivalence of Morse–Smale diffeomorphisms with a finite set of heteroclinic trajectories on irreducible 3-manifolds”, Math. Notes, 58:5 (1995), 1231–1233  mathnet  crossref  mathscinet  zmath  isi
    3. V. Z. Grines, Kh. Kh. Kalai, “Conditions of topological conjugacy of gradient-like diffeomorphisms on irreducible 3-manifolds”, Math. Notes, 59:1 (1996), 52–57  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. 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
    5. V. Z. Grines, V. S. Medvedev, “On the topological conjugacy of three-dimensional gradient-like diffeomorphisms with a trivially embedded set of separatrices of saddle fixed points”, Math. Notes, 66:6 (1999), 781–784  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Bonatti, C, “On the topological classification of gradientlike diffeomorphisms without heteroclinic curves on three-dimensional manifolds”, Doklady Mathematics, 63:2 (2001), 161  mathscinet  zmath  isi
    7. Ch. Bonatti, V. Z. Grines, V. S. Medvedev, E. Peku, “On Morse–Smale Diffeomorphisms without Heteroclinic Intersections on Three-Manifolds”, Proc. Steklov Inst. Math., 236 (2002), 58–69  mathnet  mathscinet  zmath
    8. E. V. Kruglov, E. A. Talanova, “On the Realization of Morse–Smale Diffeomorphisms with Heteroclinic Curves on a 3-Sphere”, Proc. Steklov Inst. Math., 236 (2002), 201–205  mathnet  mathscinet  zmath
    9. V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “New relations for Morse–Smale systems with trivially embedded one-dimensional separatrices”, Sb. Math., 194:7 (2003), 979–1007  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. 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
    11. V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “Peixoto Graph of Morse–Smale Diffeomorphisms on Manifolds of Dimension Greater than Three”, Proc. Steklov Inst. Math., 261 (2008), 59–83  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    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. T. M. Mitryakova, O. V. Pochinka, “Necessary and sufficient conditions for the topological conjugacy of surface diffeomorphisms with a finite number of orbits of heteroclinic tangency”, Proc. Steklov Inst. Math., 270 (2010), 194–215  mathnet  crossref  mathscinet  zmath  isi  elib
    14. V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “Classification of Morse–Smale diffeomorphisms with one-dimensional set of unstable separatrices”, Proc. Steklov Inst. Math., 270 (2010), 57–79  mathnet  crossref  mathscinet  zmath  isi  elib
    15. T. M. Mitryakova, O. V. Pochinka, “K voprosu o klassifikatsii diffeomorfizmov poverkhnostei s konechnym chislom modulei topologicheskoi sopryazhennosti”, Nelineinaya dinam., 6:1 (2010), 91–105  mathnet  elib
    16. O. V. Pochinka, “Neobkhodimye i dostatochnye usloviya topologicheskoi sopryazhennosti kaskadov Morsa–Smeila na 3-mnogoobraziyakh”, Nelineinaya dinam., 7:2 (2011), 227–238  mathnet  elib
    17. V. Z. Grines, O. V. Pochinka, “Morse–Smale cascades on 3-manifolds”, Russian Math. Surveys, 68:1 (2013), 117–173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. T. M. Mitryakova, O. V. Pochinka, “Realization of Cascades on Surfaces with Finitely Many Moduli of Topological Conjugacy”, Math. Notes, 93:6 (2013), 890–905  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. V. Z. Grines, S. H. Kapkaeva, O. V. Pochinka, “A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces”, Sb. Math., 205:10 (2014), 1387–1412  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. 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  mathnet
    21. Ch. Bonatti, V. Z. Grines, O. V. Pochinka, “Realization of Morse–Smale diffeomorphisms on $3$-manifolds”, Proc. Steklov Inst. Math., 297 (2017), 35–49  mathnet  crossref  crossref  mathscinet  isi  elib
    22. E. V. Nozdrinova, “Suschestvovanie svyaznogo kharakteristicheskogo prostranstva u gradientno-podobnykh diffeomorfizmov poverkhnostei”, Zhurnal SVMO, 19:2 (2017), 91–97  mathnet  crossref  elib
    23. V. Z. Grines, E. Ya. Gurevich, E. V. Zhuzhoma, O. V. Pochinka, “Classification of Morse–Smale systems and topological structure of the underlying manifolds”, Russian Math. Surveys, 74:1 (2019), 37–110  mathnet  crossref  crossref  adsnasa  isi  elib
    24. A. I. Morozov, O. V. Pochinka, “Kombinatornyi invariant dlya poverkhnostnykh diffeomorfizmov Morsa-Smeila s orientiruemoi geteroklinikoi”, Zhurnal SVMO, 22:1 (2020), 71–80  mathnet  crossref
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