In the present paper, the notions of similarity and conjugation of two quantum dynamical systems are defined and it is proved that similar quantum dynamical systems are conjugate. Putting forward the concepts of transitivity, minimality, chain-transitivity and equicontinuity in the context, it is proved that these notions are preserved under similarity of quantum dynamical systems. It is obtained that every minimal system is transitive, and every chain-transitive system possessing the shadowing property is transitive. Under a suitable condition it is shown that a point is minimal if and only if it is an equicontinuous point.

中文翻译：

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量子测量空间中的传递性和连续性

本文定义了两个量子动力学系统的相似性和共轭性的概念，并证明了相似的量子动力学系统是共轭的。在上下文中提出传递性、极小性、链传递性和等连续性的概念，证明这些概念在量子动力学系统的相似性下是保留的。得到每个极小系统都是可传递的，每个具有阴影性质的链传递系统都是可传递的。在合适的条件下，证明一个点是最小的当且仅当它是一个等连续点。