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arXiv · 2211.14251

On the local connectivity of attractors of Markov IFS

Nicolae Mihalache
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Abstract

We prove an extension of M. Hata's theorem [4] for planar Markov Iterated Function Systems satisfying a strong version of the Open Set Condition. More precisely, if the attractor of such a system is connected, then it is locally connected. We construct counterexamples to show that all additional hypothesis are necessary.

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Nicolae Mihalache. 2022-11-25. On the local connectivity of attractors of Markov IFS. https://arxiv.org/abs/2211.14251

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