Given a compact metric space X and a continuous function $f:X\to X$, we introduce the set function ${\mathcal{T}}_f:X\to 2^X$ given by ${\mathcal{T}}_f(x)=\mathcal{T}(\{f(x)\})$, where $2^X$ is the family of nonempty closed subsets of X and $\mathcal{T}$ is Jones' set function. We consider the dynamical system $(X,{\mathcal{T}}_f)$ and study its properties.

中文翻译：

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具有Jones设定功能的动力学 $\mathcal{Ť}$

给定一个紧凑的度量空间X和一个连续函数$F：X\to X$，我们介绍设置功能 ${\mathcal{Ť}}_F：X\to 2^X$ 由 ${\mathcal{Ť}}_F（X）=\mathcal{Ť}（\{F（X）\}）$， 在哪里 $2^X$是X和的非空封闭子集的族$\mathcal{Ť}$是琼斯的设定函数。我们考虑动力系统$（X，{\mathcal{Ť}}_F）$ 并研究其特性。