Genericity of mode-locking for quasiperiodically forced circle maps
Genericity of mode-locking for quasiperiodically forced circle maps
复制标题
准周期强制圆图锁模的通用性
DOI：
10.1016/j.aim.2019.03.023
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发表时间：
2019
影响因子：
1.7
通讯作者：
Jaeger T
中科院分区：
文献类型：
--
作者：
Wang J;Zhou Q;Jaeger T
我们发现，一个通用的准周期强迫圆同胚是锁模的：在纤维的旋转数是合理的旋转数的基础上，它是稳定的小扰动下的系统。因此，这意味着，对于一个通用的参数家庭的拟周期强迫圆同胚满足扭曲条件，图形的旋转数作为一个函数的参数是魔鬼的楼梯。
We show that a generic quasiperiodically forced circle homeomorphism is mode-locked: the rotation number in the fibres is rationally related to the rotation number in the base and it is stable under small perturbations of the system. As a consequence, this implies that for a generic parameter family of quasiperiodically forced circle homeomorphisms satisfying a twist condition, the graph of the rotation number as a function of the parameter is a devil's staircase.