Geodesic
Knot as a~complete invariant of a~Morse-Smale 3-diffeomorphism with four fixed points
Sbornik. Mathematics, Tome 214 (2023) no. 8, pp. 1140-1152

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It is known that the topological conjugacy class of a Morse-Smale flows with unique saddle is defined by the equivalence class of the Hopf knot in $\mathbb S^2\times\mathbb S^1$ that is the projection of the one-dimensional saddle separatrix onto the basin of attraction of the nodal point, and the ambient manifold of a diffeomorphism in this class is the 3-sphere. In the present paper a similar result is obtained for gradient-like diffeomorphisms with exactly two saddle points and unique heteroclinic curve. Bibliography: 11 titles.
Keywords: gradient-like diffeomorphism, topological conjugacy, Morse-Smale diffeomorphism. 
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     title = {Knot as a~complete invariant of {a~Morse-Smale} 3-diffeomorphism with four fixed points},
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O. V. Pochinka; E. A. Talanova; D. D. Shubin. Knot as a~complete invariant of a~Morse-Smale 3-diffeomorphism with four fixed points. Sbornik. Mathematics, Tome 214 (2023) no. 8, pp. 1140-1152. http://geodesic.mathdoc.fr/item/SM_2023_214_8_a5/