Bifurcations of Morse-Smale diffeomorphisms with wildly embedded separatrices. (English. Russian original) Zbl 1153.37340

Proc. Steklov Inst. Math. 256, 47-61 (2007); translation from Tr. Mat. Inst. Steklova 256, 54-69 (2007).
Summary: 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.


37D15 Morse-Smale systems
37G10 Bifurcations of singular points in dynamical systems
57M25 Knots and links in the \(3\)-sphere (MSC2010)
58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces
Full Text: DOI


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