The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate to a class of homeomorphisms for which the restriction of the map to a connected component of the non-wandering set is topologically conjugate to an orientation-preserving pseudo-Anosov homeomorphism. The ambient \(\Omega\)-conjugacy of a homeomorphism from the class with a locally direct product of a pseudo-Anosov homeomorphism and a rough transformation of the circle is proved. In addition, we prove that the centralizer of a pseudo-Anosov homeomorphisms consists of only pseudo-Anosov and periodic maps.

本文致力于研究具有由有限数量的表面吸引子和排斥子组成的非游走集的三维流形上的保向同胚。论文的主要结果涉及一类同态，其中映射对非游走集的连通分量的限制在拓扑上与保方向伪阿诺索夫同态共轭。证明了来自类的同胚与伪阿诺索夫同胚的局部直积和圆的粗变换的环境\(\Omega\)共轭。此外，我们证明了伪阿诺索夫同胚的中心化子仅由伪阿诺索夫映射和周期映射组成。