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.