Geodesic
Bifurcations of Morse--Smale Diffeomorphisms with Wildly Embedded Separatrices
Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 54-69.

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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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C. Bonatti; V. Z. Grines; V. S. Medvedev; O. V. Pochinka. Bifurcations of Morse--Smale Diffeomorphisms with Wildly Embedded Separatrices. Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 54-69. http://geodesic.mathdoc.fr/item/TRSPY_2007_256_a2/

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