Equicontinuity of the Hutchinson operator $F$ and sensitivity of $F_-$
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915756230311936 |
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| author | Sarizadeh, Aliasghar |
| author_facet | Sarizadeh, Aliasghar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equicontinuity of the Hutchinson operator $F$ and sensitivity of $F_-$ Sarizadeh, Aliasghar Dynamical Systems 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. |
| title | Equicontinuity of the Hutchinson operator $F$ and sensitivity of $F_-$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2601.18530 |