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

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