On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers

We consider a class of diffeomorphisms on 3-manifolds which satisfy S. Smale's axiom $A$ such that their nonwandering set consists of two-dimensional surface basic sets. Interrelation between dynamics of such diffeomorphism and topology of the ambient manifold is studied. Also we establish that each considered diffeomorphism is $\Omega$-conjugated with a model diffeomorphism of mapping torus. Under certain assumptions on asymptotic properties of two-dimensional invariant manifolds of points from the basic sets, we obtain necessary and sufficient conditions of topological conjugacy of structurally stable diffeomorphisms from the considered class.