在此基础上分析系统的转动数，发现转动数一般为无理数，只在某些特定条件下存在有理旋转数，从而系统作准周期运动或者周期运动。

The rotating number is generally an irrational number and only in some special conditions is a rational one, from which it can be known that the motion of the system is quasi-periodic or periodic.

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当两个比率都是有理数或无理数时，动力学局域化发生在准能带塌缩点。

When both the ratios are rational or irrational Numbers, the dynamical localization happens at the quasi-energy band collapse points.

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不是有理数的实数被称为无理数。理数的实数被称为无理数。

Real Numbers that are not in Q are called irrational.

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