M4 is regular-closed

Yutaro Himeki, Yutaka Ishii

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

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 .

本文言語英語
ページ(範囲)213-220
ページ数8
ジャーナルErgodic Theory and Dynamical Systems
40
1
DOI
出版ステータス出版済み - 1 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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