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On the equicontinuity of the Hutchinson operator
Abstract
We show that the Hutchinson operator of an Iterated Function System with an attractor is equicontinuous if and only if it is continuous; in particular, every finite Iterated Function System with an attractor has equicontinuous Hutchinson operator. We also characterize equicontinuity of Hutchinson operators generated by a natural class of continuous multifunctions in terms of continuity of their limit maps.
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BibTeX
@misc{strobin2026equicontinuity,
title = {{On the equicontinuity of the Hutchinson operator}},
author = {Filip Strobin and Piotr Szuca},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.30923},
eprint = {2605.30923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30923},
}
RIS
TY - UNPB
TI - On the equicontinuity of the Hutchinson operator
AU - Filip Strobin
AU - Piotr Szuca
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.30923
UR - https://arxiv.org/abs/2605.30923
AB - We show that the Hutchinson operator of an Iterated Function System with an attractor is equicontinuous if and only if it is continuous; in particular, every finite Iterated Function System with an attractor has equicontinuous Hutchinson operator. We also characterize equicontinuity of Hutchinson operators generated by a natural class of continuous multifunctions in terms of continuity of their limit maps.
ER -