Necessary and sufficient conditions for the topological conjugacy of 3-diffeomorphisms with heteroclinic tangencies

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.