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 Ω-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.