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Tr. Mat. Inst. Steklova, 2010, Volume 270, Pages 62–85 (Mi tm3025)  

This article is cited in 7 scientific papers (total in 7 papers)

Classification of Morse–Smale diffeomorphisms with one-dimensional set of unstable separatrices

V. Z. Grinesa, E. Ya. Gurevicha, V. S. Medvedevb

a Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
b Research Institute for Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia

Abstract: Let $M^n$ be a closed orientable manifold of dimension $n>3$. We study the class $G_1(M^n)$ of orientation-preserving Morse–Smale diffeomorphisms of $M^n$ such that the set of unstable separatrices of any $f\in G_1(M^n)$ is one-dimensional and does not contain heteroclinic intersections. We prove that the Peixoto graph (equipped with an automorphism) is a complete topological invariant for diffeomorphisms of class $G_1(M^n)$, and construct a standard representative for any class of topologically conjugate diffeomorphisms.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 270, 57–79

Bibliographic databases:

UDC: 517.938
Received in April 2009

Citation: V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “Classification of Morse–Smale diffeomorphisms with one-dimensional set of unstable separatrices”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 62–85; Proc. Steklov Inst. Math., 270 (2010), 57–79

Citation in format AMSBIB
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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. V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “Embedding in a Flow of Morse–Smale Diffeomorphisms on Manifolds of Dimension Higher than Two”, Math. Notes, 91:5 (2012), 742–745  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow”, Sb. Math., 203:12 (2012), 1761–1784  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Vyacheslav Z. Grines, Dmitry S. Malyshev, Olga V. Pochinka, Svetlana Kh. Zinina, “Efficient Algorithms for the Recognition of Topologically Conjugate Gradient-like Diffeomorhisms”, Regul. Chaotic Dyn., 21:2 (2016), 189–203  mathnet  crossref  mathscinet
    4. 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
    5. V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “An Analog of Smale's Theorem for Homeomorphisms with Regular Dynamics”, Math. Notes, 102:4 (2017), 569–574  mathnet  crossref  crossref  mathscinet  isi  elib
    6. V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “A Combinatorial Invariant of Morse–Smale Diffeomorphisms without Heteroclinic Intersections on the Sphere $S^n$, $n\ge 4$”, Math. Notes, 105:1 (2019), 132–136  mathnet  crossref  crossref  isi  elib
    7. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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