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Topological Classification of Morse–Smale Diffeomorphisms Without Heteroclinic Intersections

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We study the class G(M n) of orientation-preserving Morse–Smale diffeomorfisms on a connected closed smooth manifold Mn of dimension n ≥ 4 which is defined by the following condition: for any f ∊ G(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.

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References

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Authors and Affiliations

  1. National Research University Higher School of Economics, Lobachevsky State University of Nizhny Novgorod, 23, Gagarina pr, Nizhny Novgorod, 603950, Russia

    V. Z. Grines

  2. National Research University Higher School of Economics, 25/12, Bol’shaya Pechorskaya St, Nizhny Novgorod, 603155, Russia

    E. A. Gurevich & O. V. Pochinka

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  1. V. Z. Grines
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  2. E. A. Gurevich
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  3. O. V. Pochinka
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Correspondence to V. Z. Grines.

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Translated from Problemy Matematicheskogo Analiza 79, March 2015, pp. 73-81.

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Grines, V.Z., Gurevich, E.A. & Pochinka, O.V. Topological Classification of Morse–Smale Diffeomorphisms Without Heteroclinic Intersections. J Math Sci 208, 81–90 (2015). https://doi.org/10.1007/s10958-015-2425-2

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  • DOI: https://doi.org/10.1007/s10958-015-2425-2

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