We provide a complete characterization of periodic point free homeomorphisms of the $2$ -torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$ -torus without periodic points and exhibiting uniformly bounded rotational deviations with respect to a rational direction, we show that annularity and the geometry of its non-wandering set are the only possible obstructions for the existence of an irrational circle rotation as topological factor. Through a very precise study of the dynamics of the induced $\rho $ -centralized skew-product, we extend and generalize considerably previous results of Jäger.

中文翻译：

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周期无点同胚和非理性旋转因子

我们提供了周期无点同胚的完整表征$2$-torus 承认不合理的圆旋转作为拓扑因素。给定一个同胚$2$- 没有周期点并且相对于有理方向表现出均匀有界的旋转偏差的环面，我们证明了环形性及其非游走集的几何形状是作为拓扑因素存在无理圆旋转的唯一可能障碍。通过对感应动力学的非常精确的研究$\rho $-集中的斜积，我们扩展和概括了 Jäger 以前的结果。