Classification of Morse-Smale Diffeomorphisms on 3-Manifolds

A topological classification of the set MS(M 3) of orientation-preserving Morse-Smale diffeomorphisms f on a smooth closed orientable 3-manifold is studied. The topological classification problem is solved for any orientation-preserving Morse-Smale diffeomorphisms on closed orientable 3-manifolds. The dynamics of an arbitrary Morse-Smale diffeomorphism is represented. It is proved that Morse-Smale diffeomorphisms are topologically conjugate if and only if their schemes are equivalent. Each connected component of the manifold is a simple manifold admitting an epimorphism such that the mapping formed by these epimorphisms satisfies certain conditions. For any diffeomorphism, each connected component of the manifold obtained by the surgery of the manifold along the s-lamination is homeomorphic.