In this paper we consider a class of structurally stable diffeomorphisms with two-dimensional basic sets given on a closed 3-manifold. We prove that each such diffeomorphism is a locally direct product of a hyperbolic automorphism of the 2-torus and a rough diffeomorphism of the circle. We find algebraic criteria for topological conjugacy of the systems.

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J. Palis found necessary conditions for a Morse-Smale diffeomorphism on a closed ndimensional manifold M n to embed into a topological flow and proved that these conditions are also sufficient for n = 2. For the case n = 3 a possibility of wild embedding of closures of separatrices of saddles is an additional obstacle for Morse-Smale cascades to embed into topological flows. In this paper we show that there are no such obstructions for Morse-Smale diffeomorphisms without heteroclinic intersection given on the sphere S n , n ≥ 4, and Palis's conditions again are sufficient for such diffeomorphisms. arXiv:1806.03468v2 [math.DS] 13 Jul 2018 dation (project 17-11-01041) apart the section 4.3, which is done in frame of the Basic Research Program of HSE in 2018.

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