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Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices

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Abstract

We study bifurcations of Morse-Smale diffeomorphisms under a change of the embedding of the separatrices of saddle periodic points in the ambient 3-manifold. The results obtained are based on the following statement proved in this paper: for the 3-sphere, the space of diffeomorphisms of North Pole-South Pole type endowed with the C 1 topology is connected. This statement is shown to be false in dimension 6.

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Authors and Affiliations

  1. Institut de Mathématiques, Université de Bourgogne, BP 47870, 21078, Dijon, France

    C. Bonatti

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

    V. Z. Grines

  3. Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

    V. S. Medvedev & O. V. Pochinka

Authors
  1. C. Bonatti
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  2. V. Z. Grines
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  3. V. S. Medvedev
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  4. O. V. Pochinka
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Additional information

Original Russian Text © C. Bonatti, V.Z. Grines, V.S. Medvedev, O.V. Pochinka, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 256, pp. 54–69.

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Bonatti, C., Grines, V.Z., Medvedev, V.S. et al. Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. Proc. Steklov Inst. Math. 256, 47–61 (2007). https://doi.org/10.1134/S0081543807010038

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  • DOI: https://doi.org/10.1134/S0081543807010038

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