This paper establishes topological (equi-)semiconjugacy and (equi-) conjugacy between induced non-autonomous set-valued systems and subshifts of finite type. First, some necessary and sufficient conditions are given for a non-autonomous discrete system to be topologically semiconjugate or conjugate to a subshift of finite type. Further, several sufficient conditions for it to be topologically equi-semiconjugate or equi-conjugate to a subshift of finite type are obtained. Consequently, estimations of topological entropy and several criteria of Li–Yorke chaos and distributional chaos in a sequence are derived. Second, the relationships of several related dynamical behaviors between the non-autonomous discrete system and its induced set-valued system are investigated. Based on these results, the paper furthermore establishes the topological (equi-)semiconjugacy and (equi-)conjugacy between induced set-valued systems and subshifts of finite type. Consequently, estimations of the topological entropy for the induced set-valued system are obtained, and several criteria of Li–Yorke chaos and distributional chaos in a sequence are established. Some of these results not only extend the existing related results for autonomous discrete systems to non-autonomous discrete systems, but also relax the assumptions of the counterparts in the literature. Two examples are finally provided for illustration.

中文翻译：

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诱导非自治集值系统与有限类型子移位之间的拓扑共轭

本文建立了诱导的非自治集值系统与有限类型子移位之间的拓扑（等价）半共轭性和（等价）共轭性。首先，为非自治离散系统在拓扑上半共轭或共轭到有限类型的子移位给出了一些必要和充分的条件。此外，获得了几个足够的条件，使其成为拓扑上的半半共轭或有限共轭的亚共轭。因此，得出了序列中Li-Yorke混沌和分布混沌的拓扑熵估计和几个判据。其次，研究了非自治离散系统与其诱导集值系统之间几种相关动力学行为的关系。根据这些结果，本文进一步建立了诱导集值系统与有限类型子移位之间的拓扑（等价）半共轭性和（等价）共轭性。因此，获得了对诱导集值系统的拓扑熵的估计，并建立了序列中的Li-Yorke混沌和分布混沌的几个准则。这些结果中的一些不仅将现有的独立离散系统的相关结果扩展到非自治离散系统，而且还放宽了文献中对应对象的假设。最后提供两个示例进行说明。并建立了李约克混沌和分布混沌的几个判据。这些结果中的一些不仅将现有的独立离散系统的相关结果扩展到非自治离散系统，而且还放宽了文献中对应对象的假设。最后提供两个示例进行说明。并建立了李约克混沌和分布混沌的几个判据。这些结果中的一些不仅将现有的独立离散系统的相关结果扩展到非自治离散系统，而且还放宽了文献中对应对象的假设。最后提供两个示例进行说明。