Dynamics of 3-Homeomorphisms with Two-Dimensional Attractors and Repellers

On closed orientable 3-manifolds, we consider a class G of homeomorphisms such that the nonwandering set of each f ∈ G is the finite union of surfaces such that the restriction of some power f k on each of these surfaces is a pseudo-Anosov homeomorphism. We prove that homeomorphisms of class G exist only on 3-manifolds of the form S g × ℝ/ (J(z),r−1) , where J : S g → S g is either a pseudo-Anosov homeomorphism of the surface S g of genus g > 1 or a periodic homeomorphism commuting with some pseudo-Anosov homeomorphism. On such a manifold, we construct model homeomorphisms and find necessary and sufficient conditions for topological conjugacy of model mappings.