论文标题
准周期强迫Arnold Circle Maps的模式锁定特性的密度
Density of mode-locking property for quasi-periodically forced Arnold circle maps
论文作者
论文摘要
我们表明，具有拓扑通用的强迫函数的准周期强迫圆形图的家族的模式锁定区域是密集的。这对\ cite {dgo}的某些数值观察进行了严格的验证，以实现此类强迫函数。更普遍地，在基本图上的某些一般条件下，我们显示了装有拓扑结构的动态强制图（定义在\ cite {Zha}中）之间的模式锁定特性的密度，该拓扑比$ c^0 $拓扑结构强得多，与光滑的纤维图兼容。对于准周期基映射，我们的结果概述了\ cite {abd，wzj，zha}的主要结果。
We show that the mode-locking region of the family of quasi-periodically forced Arnold circle maps with a topologically generic forcing function is dense. This gives a rigorous verification of certain numerical observations in \cite{DGO} for such forcing functions. More generally, under some general conditions on the base map, we show the density of the mode-locking property among dynamically forced maps (defined in \cite{Zha}) equipped with a topology that is much stronger than the $C^0$ topology, compatible with smooth fiber maps. For quasi-periodic base maps, our result generalizes the main results in \cite{ABD, WZJ, Zha}.
