| Abstract: |
| Let $(X,d)$ be a compact metric space and $f$ be a continuous surjection on $X$. The dynamical system $(X,f)$ induces the system $(2^X,f_{\ast})$ where $2^X$ is the set of all non-empty closed subsets of $X$ with the Hausdorff metric.
The enveloping semigroup of $(X,f)$ is the closure of $\lbrace f^n: n\in \mathbb{N}\rbrace$ in $X^X$ with the topology of pointwise convergence. We study some comparison between the enveloping semigroups $E(X)$ and $E(2^X)$. |
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