On the local connectivity of attractors of Markov IFS
Volume 264 / 2024
Fundamenta Mathematicae 264 (2024), 309-319
MSC: Primary 37B10; Secondary 37F40, 37B45
DOI: 10.4064/fm298-11-2023
Published online: 21 February 2024
Abstract
We prove an extension of M. Hata’s theorem [Japan J. Appl. Math. 2 (1985), 381–414] 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 the additional hypotheses are necessary.
