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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