M4 is regular-closed

Yutaro Himeki, Yutaka Ishii

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    For each , we investigate a family of iterated function systems which is parameterized by a common contraction ratio <![CDATA[$s\in \mathbb{D}^{\times }\equiv \{s\in \mathbb{C}:0<|s| and possesses a rotational symmetry of order . Let be the locus of contraction ratio for which the corresponding self-similar set is connected. The purpose of this paper is to show that is regular-closed, that is, holds for . This gives a new result for and a simple geometric proof of the previously known result by Bandt and Hung [Fractal -gons and their Mandelbrot sets. NonlinearityA 21 (2008, 2653-2670] for .

    Original languageEnglish
    Pages (from-to)213-220
    Number of pages8
    JournalErgodic Theory and Dynamical Systems
    Issue number1
    Publication statusPublished - Jan 1 2020

    All Science Journal Classification (ASJC) codes

    • General Mathematics
    • Applied Mathematics


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