A self-similar set with non-locally connected components

2024/03/29 by Jian-Ci Xiao, Xiao, Jian-Ci
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Primary 28A80 #Secondary 54D05

paper · pdf · doi:10.48550/arxiv.2403.19999

openalex publication_date 2024/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Luo, Rao and Xiong [Topol. Appl. 322 (2022), 108271] conjectured that if a planar self-similar iterated function system with the open set condition does not involve rotations or reflections, then every connected component of the attractor is locally connected. We create a homogeneous counterexample of Lalley-Gatzouras type, which disproves this conjecture.

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