Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four fixed points

Abstract

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.