论文标题
在不可裁定的周期轨道和有限偏差上
On Non-contractible Periodic Orbits and Bounded Deviations
论文作者
论文摘要
我们为表面同位素类别的表面同态呈现二分法。我们表明，在没有退化的固定点集的情况下，要么在通用覆盖空间中提起的动力学的非随机点的轨道直径上存在均匀的结合，要么该地图具有非合同的周期性点。然后，我们使用该新工具来表征无需不可扣除周期点的圆环的区域动力学，表明如果固定点集是非分类的，则升起的动力学是统一的，或者提起的映射具有单个强的非理性动力学方向。
We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for the lifted dynamics in the universal covering space, or the map has non-contractible periodic points. We then use this new tool to characterize the dynamics of area preserving homeomorphisms of the torus without non-contractible periodic points, showing that if the fixed point set is non-degenerate, then either the lifted dynamics is uniformly bounded, or the lifted map has a single strong irrational dynamical direction.
