Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices |
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| Authors: | C Bonatti V Z Grines V S Medvedev O V Pochinka |
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| Institution: | (1) Institut de Mathématiques, Université de Bourgogne, BP 47870, 21078 Dijon, France;(2) Nizhni Novgorod State Agricultural Academy, pr. Gagarina 97, Nizhni Novgorod, 603107, Russia;(3) Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia |
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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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