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Journal of Mathematical Sciences

, Volume 208, Issue 1, pp 81–90 | Cite as

Topological Classification of Morse–Smale Diffeomorphisms Without Heteroclinic Intersections

  • V. Z. GrinesEmail author
  • E. A. Gurevich
  • O. V. Pochinka
Article

We study the class G(M n ) of orientation-preserving Morse–Smale diffeomorfisms on a connected closed smooth manifold M n of dimension n ≥ 4 which is defined by the following condition: for any fG(M n ) the invariant manifolds of saddle periodic points have dimension 1 and (n − 1) and contain no heteroclinic intersections. For diffeomorfisms in G(M n ) we establish the topoligical type of the supporting manifold which is determined by the relation between the numbers of saddle and node periodic orbits and obtain necessary and sufficient conditions for topological conjugacy. Bibliography: 14 titles.

Keywords

Manifold Saddle Point Vector Bundle Periodic Point Invariant Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. Z. Grines
    • 1
    Email author
  • E. A. Gurevich
    • 2
  • O. V. Pochinka
    • 2
  1. 1.National Research University Higher School of EconomicsLobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  2. 2.National Research University Higher School of EconomicsNizhny NovgorodRussia

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