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Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three

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Abstract

Let M n be a closed orientable manifold of dimension greater than three and G 1(M n) be the class of orientation-preserving Morse-Smale diffeomorphisms on M n such that the set of unstable separatrices of every f ∈ G 1(M n) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G 1(M n).

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Authors and Affiliations

  1. Nizhni Novgorod State Agricultural Academy, pr. Gagarina 97, Nizhni Novgorod, 603107, Russia

    V. Z. Grines

  2. State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod, 603107, Russia

    E. Ya. Gurevich

  3. Research Institute for Applied Mathematics and Cybernetics, ul. Ul’yanova 10, Nizhni Novgorod, 603005, Russia

    V. S. Medvedev

Authors
  1. V. Z. Grines
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  2. E. Ya. Gurevich
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  3. V. S. Medvedev
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Correspondence to V. Z. Grines.

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Original Russian Text © V.Z. Grines, E.Ya. Gurevich, V.S. Medvedev, 2008, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 261, pp. 61–86.

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Grines, V.Z., Gurevich, E.Y. & Medvedev, V.S. Peixoto graph of Morse-Smale diffeomorphisms on manifolds of dimension greater than three. Proc. Steklov Inst. Math. 261, 59–83 (2008). https://doi.org/10.1134/S0081543808020065

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