Topological conjugacy plays an important role in simplifying the systems and equations in the research of dynamical systems and functional equations. In this paper, we deal with increasing upper semi-continuous multifunctions with finitely many set-valued points. Some sufficient and necessary conditions are given for the topological conjugate relation between those multifunctions, and the methods of construction for all conjugacies are also presented. Moreover, as an application, our results are applied to study the problem of iterative roots for the multifunctions with a unique set-valued point.

中文翻译：

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具有有限多个集合值点的多功能的拓扑共轭及其在迭代根中的应用

拓扑共轭在动力系统和泛函方程研究中对简化系统和方程具有重要作用。在本文中，我们处理具有有限多个集合值点的递增上半连续函数。给出了这些多重函数之间拓扑共轭关系的一些充分必要条件，并给出了所有共轭的构造方法。此外，作为一个应用，我们的结果被应用于研究具有唯一集值点的多功能的迭代根问题。