Geodesic
Necessary and sufficient conditions for the topological conjugacy of 3-diffeomorphisms with heteroclinic tangencies
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 1, pp. 83-102.

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In this paper we consider a class of three-dimensional diffeomorphisms that differ from gradient-like systems through the presence of heteroclinic tangencies. It is well known that such cascades are not structurally stable. However, here we find a complete system of topological invariants for a certain meaningful class of such diffeomorphisms. 
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T. M. Mitryakova; O. V. Pochinka. Necessary and sufficient conditions for the topological conjugacy of 3-diffeomorphisms with heteroclinic tangencies. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 1, pp. 83-102. http://geodesic.mathdoc.fr/item/MMO_2016_77_1_a2/

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