Work

A self-similar set with non-locally connected components

Year: 2024

Type: article

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.

Source: Journal of Fractal Geometry Mathematics of Fractals and Related Topics

DOI: 10.4171/jfg/148

Author: Jian-Ci Xiao

Institutions: Chinese University of Hong Kong, Nanjing University of Aeronautics and Astronautics

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Zhejiang University

OpenAlex ID: W4401615620

FWCI:

Cites:

Cited by:

Related to: 10