Equicontinuity of the Hutchinson operator $F$ and sensitivity of $F_{-}$

Abstract

For an iterated function system $\mathcal{F}=\{f_1,\dots ,f_k\}$ of homeomorphisms on a compact metric space $(X,d)$, write ${\mathcal{F}}_{-}=\{f_1^{-1},\dots ,f_k^{-1}\}$. The objective of this paper is to illustrate an iterated function system $\mathcal{F}$ of homeomorphisms on the circle that the Hutchinson operator of $\mathcal{F}$ is equicontinuous, but the Hutchinson operator of ${\mathcal{F}}_{-}$ is sensitive.