圆映射理论与一维周期运动光腔问题
Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
摘要：
我们考虑电磁场在一个腔的周期性振荡的完美反射边界，并表明，数学理论的圆映射导致几个物理预测。值得注意的是，众所周知的结果在理论的圆映射（我们简要回顾）意味着有间隔的参数，在那里的波在腔中得到集中的波包的能量呈指数增长。即使这些区间是密集的反射边界的典型运动，在补充有一个积极的措施设置参数的能量仍然有界。
英文摘要：
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.
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