Let (X, d) be a compact metric space and φ: X⊸X be a multivalued map. At first, we will extend for these maps the notions of a topological entropy and Robinson’s chaos from a single-valued into a multivalued setting and show their basic properties. Then, for a subclass of multivalued continuous maps with compact values, we will clarify their relationship to the induced (hyper)maps ${\phi }^{*}:\mathcal{K}\left(X\right)\to \mathcal{K}\left(X\right)$ in the hyperspace $(\mathcal{K}\left(X\right),d_H),$ endowed with the Hausdorff metric d_H, where $\mathcal{K}\left(X\right)$ consists of all compact subsets of X. Concretely, we will show that a positive topological entropy h(φ) of φ implies a positive topological entropy h(φ*) of φ*. On the other hand, Robinson’s chaos to φ* implies in a reverse way Robinson’s chaos to φ.

设（X，d）是紧致度量空间和φ：X ⊸ X是一个多值图。首先，我们将这些映射的拓扑熵和Robinson混沌的概念从单值扩展为多值设置，并显示其基本属性。然后，对于具有紧凑值的多值连续映射的子类，我们将阐明它们与诱导（超）映射的关系。${\phi }^{*}：\mathcal{ķ}（X）\to \mathcal{ķ}（X）$ 在超空间 $（\mathcal{ķ}（X），d_H），$赋予Hausdorff指标d _H，其中$\mathcal{ķ}（X）$由X的所有紧凑子集组成。具体而言，我们将证明一个正拓扑熵^ h φ的（φ）意味着正拓扑熵^ h φ*的（φ*）。另一方面，罗宾逊对φ*的混乱暗示着罗宾逊对φ的混乱。